OP, have you gotten enough advice to confuse you even more?
I'll add my experience to the rest. The prereq for mine was basic college alg. I had special circumstances & all my prereqs for everything were waived. No, I hadn't taken any college level math. If you understand plain ole arithmetic and high school alg. basics, you may be fine.
Another poster mentioned that chem is just math in context. That makes it so much easier because when you know how things relate, the way to solve them just makes sense. The prof. used calculus in the explanations often, but we didn't have to know it for the course. However, once again, it's easy to understand in context. Books tend to contain loads of problem sets. Just do them until you are comfortable and they're second nature.
I did things bass ackwards and took the chem before the math courses. Worked out well because I think doing that made the math classes a breeze.
So no, you won't definitely do poorly just because you don't feel up to par on the math. If you allow a fear of math to get in the way, that might adversely affect you, but if you tend to learn well in context, and go to the effort of doing problem sets as much as you need to, you'll be fine. Your level of interest in and dedication to mastering the subject may be the greater determining factors in how well you do.