I'm just guessing here as it is not a normal English expression - it sounds like something that has been made up for the film.
A 'chaser' is a drink. It is normally a 'short', or a spirit, such as sambuca, that people drink in one mouthful after they have had a different drink, such as a pint of lager. Pretty disgusting.
So I guess a 'high fat chaser' would mean that Garfield is bored of being on his diet and so he is going to eat or drink something with a lot of fat in it! Perhaps a milkshake??!
- For Teachers