[doctorwho19]

Would two years of Calculus prior to the semester I take P-Chem and then co-enrollment with Calc III be enough? Technically only two years of Calculus are required for the major at my college-is continuing on to Calc III even worth it?

[stewie griffin]

I took AP calculus in high school and tested out of Calc I and II. Calc III wasn't a prerequisite for physical chemistry, and since I knew I wanted to do organic chemistry in graduate school, I didn't bother with Calc III.
I was able to get thru physical chemistry just fine. Got A's in both thermodynamics and also quantum mechanics, though I will admit I didn't really know what I was doing with partial derivatives. I was smart enough to figure out how to do the math to get the answer, but at times I didn't really "know" what I was actually doing. In retrospect I wish I had taken calc III so I had I better understanding of physical chemistry. Thermodynamics pop up all over the place and it's good to have a solid background in it.
Just depends what your goals and future plans are...

[Corribus]

Knowledge of integrals and derivatives is a must.  Partial derivatives (multivariable calculus) are frequently used as well.  I wouldn't suggest taking P chem without a solid background in these.  Knowledge of matrix algebra and differential equations is useful, though how much you encounter will depend on a lot on your instructor, and typically you are taught what you need to know in the course itself.