does your cat eat really fast and then throws up?
how old is your cat?
what kind of food do you give your cat?
If it does eat really fast or a lot and then throws up, your solution is very simple: give just a little bit of food at a time, several times a day and make sure the cat is in a quiet area with no one to disturb. Gobbling up too much food or really fast can cause to vomit for some cats (especially older)
if your cat is older than 6 years old, you have to switch it to lighter food especially if it's an indoor cat. Perhaps he's throwing up because the food is too rich for his body! Try food specially formulated for older cats.
if your cat has no other symptom than throwing up right after eating, that's the only thing i can think of. ( i am not a vet, so it could be an array of things i know nothing about, just sharing my thoughts)
I'm not sure if cats can develop food allergies with age, but if you are giving food that is chicken flavored, try to get food that contains NO chicken products whatsoever. Some cats are sensitive to it. I think most lamb flavored dry food doesn't have traces of chicken, but ask at your local pet store or call your vet to know.
There shouldn't be a fee to ask on the phone to your vet what kind of food is easiest on the stomach of a cat!