Does gravity affect the rate of a chemical reaction?
It sort of depends what you mean. If by "affect the rate of a chemical reaction", you mean affect the individual steps of some overall reaction as to slow them down, then no, gravity definitely has no effect at all.

This is simply because the gravitational force is so much weaker than the electrostatic force, which will dominate all interactions relevant in chemical reactions, that it does not have sufficient time to make any appreciable difference in the behavior of molecules or atoms.

A kind of standard way of demonstrating this is by imagining a situation in which it is guaranteed that electromagnetism will be stronger than gravity, which is all normal situations in chemistry, and then plugging the numbers into Coulomb's law or Newton's law of gravity.

This, however, is contrived because there are situations where gravity is stronger than electromagnetic interactions. Just never in chemistry. This article does a pretty good job of explaining this, and pointing out that the ratio of forces can really be anything at all.

The key reason gravity will never be relevant to individual chemical processes, and hence never affect the rate, is that the external gravitational field will affect the molecules equally once they are close enough to interact electromagnetically. And once they are interacting electromagnetically, it is guaranteed this force will be much, much stronger than the gravitational interaction between them because both follows the same $1/r^2$ law, so it is just a matter of comparing the proportionality constants which go in front of the law, and inputting some masses and charges characteristic to the situation. The article I linked does provide a context in which the gravitational force dominates the electromagnetic force, so this is possible.

So, no individual rates will not be affected. It's fun to imagine how gravity could affect macroscopic equilibria though, so let's think about that.

Given sufficient time, gravity is very good at organizing things in a particular way. For instance, if you imagine two planets which have atmospheres that at some time are exactly identical, but one planet is much more massive than the other one, I don't think anyone would contend that these atmospheres will look exactly the same after a long time. For instance, the escape velocity of an object is $\sqrt{2rg}$, $r$ being the radius of the planet and $g$ the gravitational constant of acceleration. If $g$ is increased significantly, then you would not lose nearly as much hydrogen from the atmosphere, which could affect the location of certain chemical equilibria in the atmosphere. The atmosphere as a whole would be kept much closer to the planet, which could also be relevant.

All of this is kind of contrived, however. The point is that gravity will only really affect chemistry in how it organizes materials, but cannot affect the individual rates.