grammar question

Chase is correct, I am not sure why but I think it has something to do with seeing and chasing happening at the same time, or just that the action is reported. If you said I saw a cat and it chased a rat, it would be in past tense... think of other examples and it is quite clear to the inner grammar ear that 'chase' is correct, like I learned how to drive a car, he heard his mother scream, etc.

As it is a past indefinite tense in which second form of verb will apply.... the word "saw" is already being used in the sentence, so after that all verbs will take first form of verb...

I saw a cat chasing a rat down the drain.

This means that you did not see the complet action, from the beginning to end.

I saw a cat chase a rat down the drain.

This means that you saw complete action, from beginning to end.