How can I get my teenage son to help around the house more? He is pretty good about it,
but rarely does things without prompting.

you have a very typical teenage son! - well except to say that he is pretty good about it - that seems to be unusual!
Get used to the prompting, and be glad that at least he is being helpful!

Stop prompting. Everything he has comes from you. Without you, he has no roof over his head, no clothing, no electronic media. Any day that he doesn't remember to do what he is supposed to do, take back something that is yours. Remember, you are training the husband of your future daughter-in-law and the father of your future grandchildren. If you want him to marry and stay married, if you want him to be a good father, it is up to you to teach him now that there are consequences for not living up to your responsibilities. Right now, it means losing his cell phone for a week. In ten years, it might mean divorce court.

I don't think taking things away will help. I think that will just make him resentful towards you. I think everyone likes to feel appreciated. Maybe something as simple as a thank you might help unless you've already got that covered. Maybe it's that you reminding him when he already has it planned out. Maybe you could make up a schedule with him (that way he can plan chores around other things he might like to do) so that you know he'll load the dishwasher at 4:30 and you don't remind him before that because you think he's just being lazy.

Use imaginative parenting. Does he have a cell phone? That can be taken away. Does he have an xbox? That can be unplugged. Does he have a computer? That can be removed. Does he get to drive the car? Keys can be confiscated.