My understanding is to teach a given subject at secondary level, you need to have done a degree with at least 50% of that subject making up the course, for example in a joint honours course, or some courses such as engineering or physics where maths might make up half the course content by default. Since you are presumably doing a single honours course in psychology, and there is no chemistry content otherwise in a psychology degree, I think you would not be able to do a PGCE in Chemistry and teach that subject directly.
However, if your course has less than half of it's content being a given subject you might be able to do an Subject Knowledge Enhancement (SKE) to bridge the gap. I'm not sure how plausible that is as an option if your first degree has
no subject relevant content in it though (this seems more common for, as the above example, engineering or physics where half the course is
not maths, but they still do a lot of it and they just need to bridge a smaller gap to prepare for teaching mathematics at secondary school level).
As it is, I do not think that degree would be a suitable background if you wanted to teach chemistry at secondary school level. A chemistry degree would obviously be most relevant. However something else with a lot of chemistry content plus an SKE, such as a degree in biochemistry, or at a stretch perhaps pharmacology or chemical engineering, may suffice.
@04MR17 might know some more about the format of qualifying for secondary school teaching?