I do a couple of different things, depending on the chore.
I will ask him if he would rather do a different chore (one of mine) and I can take over the garbage. If he says no, then I do suggest the trash getting taken out immediately so I have room to put the packaging for when I cook dinner. Otherwise dinner will have to wait due to the uncleanliness of a full trash can and such around my hands, sleeves, etc. while preparing food.
Long term--I do give him a very appreciative and sincere compliment when he does things without reminders, on a whim or just because. It makes him want more....then he does it without reminders. And I have noticed him giving it back sometimes.