You're welcome, glad to help
A chiller will be tough to run. To start with, since we're talking about a device that uses a compressor, I would definitely get a pure sine wave inverter. Modified sine wave might be fine for aquarium pumps that are submerged in liquid, but with something as expensive and complex as a chiller, I would want pretty clean power going into it.
There are two big issue here that will need addressing. The first is the start-up current. As you mentioned, it's probably going to be pretty high with a compressor. Some refrigerators draw up to 13A on startup, which is almost 1600W at 120VAC. Most modern refrigerators use about 100W - 200W when running, so the inrush current in this case is huge. There aren't many good ways to measure start up current without a high-quality multimeter, like a Fluke with an INRUSH mode. I don't think a Kill-A-Watt will tell you in-rush current. You could switch to the WATTS mode and hope you see the inrush on the meter, but this may not work if the start-up is fast. You might be able to call the chiller manufacturer and ask how much inrush current they expect with that chiller. You could also just skip all that and get a really high capacity (2,000W+) inverter. But, if you're going with a PSW inverter, this is going to get costly fast. Plus, if you undersize the inverter, it won't run your load at all.
This 2,000W model from Renogy has a 4kW surge rating. If your chiller is 400W or smaller, this allows for a 10X current draw at startup, which I think is reasonable. Any larger than 400W though might be pushing it.
I'm honestly not sure how I would handle this one. Measuring inrush current with a multimeter is probably the most accurate way to do it, but it requires messing around with AC voltage and requires a good multimeter.
@Brew12 has a lot more electrical experience than I do.
@Brew12 do you have any thoughts on how best to measure the inrush current for a chiller?
The other big issue is battery power. So assuming we've dealt with the large inrush of current, we now have to power the thing. A lot of chillers use over 300W. Some of the 1/2HP models report using up to 7A (that's 840W at 120VAC). If we split the difference and assume the chiller uses around 500W and you have 50W in pumps you want to run, that's still a huge load. After accounting for inefficiency and DOD, that's 252 amps to run the load for 4 hours. You would need at least 3 of the battery I put in my previous post to run this system for just 4 hours. That does assume the chiller will be running 100% of the time, which might not be the case. But, if your AC is off and the house is heating up, the chiller might just be running continuously.
I think the best place to start is getting a Kill-A-Watt and measuring how much power your equipment uses. Try measuring how many watts the chiller draws while it's on so that you can estimate that it's running 100% of the time.