Possible? Yes. Do you need to to some prep work before hand? You must!

Now, to your answer. The simple reason latex does not adhere to alkyd or oil based paint is the hardness of the finish. To resolve this issue you will need to follow basic steps of Cleaning, Sanding, Priming, and applying the finish coats.

Kilz is not an acceptable primer for this situation. Check your local paint dealer for a primer designed for your challenge. Clean the surface with TSP (Tri-Sodium Phosphate) rinse and sand to texture the existing finish. Prime and finish with 2 coats of latex. Seems to be a lot of trouble, but once you have done this, latex it is from there on.