I want to replace a ceiling light fixture with a ceiling fan w/light kit. The light is on a 3-way circuit. The fan came with a UC-9050T wall remote. What I would like to do is control the fan light kit with the 3-way switches and control the fan with the remote. Is this possible? If so, how? Thank you.

No can do with what you have. If the 3 ways are all off for the light then there is no power reaching the remote receiver. Although you have a 3 way now the result is only one hot wire gets up to the box. To do what you want you need 2 hots, one hot 24/7 and the other hot when at least one 3 way is ON.

Whether you can do that depends on how the fixture was wired. If the power was taken to the light fixture (ceiling box) you do what you want. If power was taken to the switch you can't.

Tell us what wires are in the ceiling box.