Does chemotherapy affect eyesight?

Some. Transiently many patients will have some trouble focusing; somewhat like when ones eyes are tired. Steroids which are commonly used with chemotherapy drugs can increase cataract formation, which used to be a leading cause of poor vision, but now can almost always be fixed quite easily.
It can, yes. Most effects on the eyes are minor and temporary, such as dry eyes, watery eyes, and irritation (called "conjunctivitis"); but chemo can cause more serious problems, like cataracts. You should notify your oncologist immediately if you notice any change at all in your eyesight.