My nitrates measure 0. I've always wanted 20 to 25 schooling fish in my reef tank and thought that green chromis would be the perfect solution. I didn't know that they were that aggressive toward each other, had always read that they were a peaceful fish and best kept in groups of 5 or more. Is there any schooling fish out there that might work better? I've always liked the color of the green chromis.
Chromies are very often peaceful to "others" but this kind of "aggression among the pack" is a common, if not universal, trait among the schooling fish that we all try to keep - Anthias, Tangs and Chromies included. You will probably have better luck in the long run maintaining one, than a school (depending on what you're trying to acheive, of course.) Five or more (and odd better than even beyond five) is always a good bet as Robert already mentioned, as that makes multiple "targets" more likely at the "low end of the pack" to disperse the assault from the "alphas". This is a very good theory which you will see play out in the tank to varying extents, and I'm sure if fish could read the Chromies would be 100% "with us" on the plan and never actually kill the "little guys"....but their reading skillz are not great, so often you'll still end up with only one in the long run.

The reality that we're up against with our rules of thumb like "five or more" is that in nature, these fish typically (but not always) school in the thousands - maybe even high in the thousands. We're never going to fully duplicate that kind of social system.
I'd like to thank everyone for their input. It seems that several have had the same experience with green chromis as I have. Based on the feedback it doesn't seem like I've done anything wrong. As much as I would like to keep a nice school of chromis in my tank, buying fish just to see them all die off in a matter of a week is neither humane or financially savvy in my book. I guess I'll have to try another species. Damsels tend to be too aggressive and they don't school. I don't know if there is a hardier chromis or not. I like anthias but when they die that really hurts the wallet. For now I think I'll build up my coral and add fish later. My corals are doing fine.
Schooling Fish
As noted already, "schooling" is actually sort of a tough category in saltwater. Especially if you're used to the hundreds of great options on the freshwater side of the hobby. You might look into a school of Cardinals...there are a few to consider: threadfin (aka blue-eye), Banggai and Pajama are a few of the more common ones. The Cardinals have their own issues though - extremely shy and not very active are typical traits. Not really what most "schooling fish fans" are after.
Schooling dartfish (also with their issue - jumpers!) might be another possibility. A large colony of Barnacle Blennies would be a really fun way to think outside of the box on this! I've got three of them in my 50 gallon....great, sociable, cryptic-but-not-shy, and a real hoot during feeding time.....they strike to the food and back to their hole like a tiny bolt of lightning! Not schoolers in the traditional sense at all though.
Honestly, the best schooling fish I've every seen in a tank in person is the
Klein's Butterflyfish. They are extremely strong schoolers - much more inline with the peacefulness and "togetherness" a veteran of freshwater might expect - and I've never heard of them bothering another fish (aside from other butterflies.....Klein's will be your only Butterfly specie.) In your tank - 240 is a great size! - I would do a school of at least five - more would be very beautiful. I've kept them in reefs (and known several others who did as well) and if you don't let them starve they will most likely leave your corals alone or only nip and do no great damage. I've known only one story personally of them eating coral and it was while the owner was away and they were going unfed....a few zoos and a head of two of acan were gone when he got back. This was an isolated case in my experience, and clearly not a mystery....so I consider these reef-safe fish with the caveats explained. And if you're after a great schooling fish, I think these caveats would be well worth "living with".

(As a "cherry on top" these fish are also usually fairly inexpensive!)
Shipping/Disease Issue
A few other thoughts on the good possibility of communicable disease that Robert brought up. Anytime a very high-metabolism fish like these guys ship with more than one or so per bag (maybe even with only one!), ammonia and O2 are going to be potential issues. Lack of O2 will weaken or kill a fish, of course. Any ammonia issue is going to lead to (at minimum) gill burning, worse can be impact to other organs. This damage leads to infection quite often IMO (technically impossible to detect AFAIK...and not instantly fatal). The more fish per bag, the more likely. A trip from the LFS to home is a different story....temperature is typically more favorably controlled, and of course the trip home is extremely short by comparison. This is the way to go for fish purchasing if you were to ask me - the LFS. You always see what you get beforehand (and the tank it came from), so you can always opt to wait on the next shipment - or even to build your school slowly from multiple LFS shipments over the course of a week (or few weeks).
Acclimation
Beyond the shipping issues, I would rarely if ever suggest acclimating fish for as long a period as you indicate you did. (3hrs, I think?) It's overkill and needlessly opens your fish up to more possibilities of harm - mostly general stress and ammonia buildup in the acclimation water. (Smaller fish are more susceptible and as already noted, high metabolism fish generate more, faster.)
First, for my suggestion, decent "normal" water in the tank is a prerequisite. Assuming the bag water the new fish come in isn't excessively fouled and pH isn't wildly different from the tank's, I would do a simple drip acclimation for about 10 minutes or so....and try to get a mix of 50:50 tank water to bag water before you transfer them (but none of the acclimation water!) to the tank. I'm sure there are sensible exceptions for this procedure, but they should be exceedingly rare. One exception is if the bag water is excessively fouled. This would mean any noticeable smell (our noses are acutely tuned for ammonia, so trust your nose!) or yellowing of the water. Depending on the apparent stress level of the animal, I would either rush the 50:50 mixing by doing water changes every minute or so in place of the dripping....or simply remove the animal directly from the bag water to your tank via net. In reality, almost all common fish will do just fine though this "non-acclimation" if the tank water is healthy and "well seasoned" (i.e. a well cared for, mature system)...especially if remaining in polluted bag water is the option. In nearly all cases, shorter acclimations are better than long.
Good luck!
-Matt
P.S. Ammonia neutralizer (often in the form of a dechlorinator) isn't a bad thing to have on hand for those emergency situations when a new bag of fish comes in very nasty, but for some reason you are afraid just to remove him to the tank directly. (Suspicion of disease, for example....some shipments are just rough!) I would use the neutralizer and the rapid 50:50 acclimation together in this scenario if possible.