It depends on the rating of the power strip. It's usually not a good idea because chillers can be such a large load that it has the potential to overload the power strip.
Check amp rating of chiller. May say RLA and then a number. Stands for run load amps. Check amp rating on power strip.
Add the rest of the components plugged into power strip. If it exceeds the amp rating for the power strip then get one with your needed amp rating.
Thanks for the info everyone...I was going to run it into a power strip for convenience to adjust something else. I'm going to play it safe and keep it plugged into the wall.