Physical Chemistry calculus is pretty tame at an introductory level. Thermodynamics is primarily partial derivatives and very simple integrals.
Second quarter is statistical chemistry, electrochemistry and kinetics for us. If your instructor wants, he could give you some time consuming systems of differential equations but I doubt you'll be asked to actually do any. Other wise, kinetic theory and transport were more probability than calculus. Electrochemistry was algebra once derivatives were done.
Quantum can be a whole different ball game though. In a chemistry department, it probably uses some multivariable calculus but it's mostly linear algebra and differential equations (learn matrix diaganolization if you have not).
If anything, I'd say review linear algebra.