Gm wired the relay for the choke thru the allternator. Even if the alternator is charging, it may have a problem Get the alternator checked out by a reputable shop. Have them look at diode ripple .
Short version: alt has 3 windiings and 6 diodes. Lose one diode= loss of one winding. Alt still charges, just not as well. Still shows a charge, but not as good as before. If the damaged diode happens to be the one that feeds the choke relay, choke light comes on. Look at a wiring diagram. If you are thinking " What the F!!!!", all I can say is : Been there, fixed that.