You can, you would have to sand a little first so that the paint sticks!
Lightly sand with 220 grit sandpaper to remove the shine. Prime with Kilz primer then paint.
Hi Linda. As Judi said you would need to sand a bit, but you also need to use an oil or alkyd based paint (better for furniture anyway). If you want to use a water based, there's a longer process to use, but it can be done. good luck.