My boyfriends son who is four now had exactly this problem. I used to actually get really embarassed by it because I didn't know any other kids who did it nearly as badly. It was pretty much a constant dribble and he seemed completely unaware of it, only wiping it when we told him to and if we saw it start to come out of his mouth we'd actually have to tell him to swallow it.
I used to really worry that he'd never grow out of it, that when he was eighteen I'd still be having to tell him when to swallow his dribble! Of course though he has grown out of it now, he did a long while ago and now I can't believe how much I used to worry about it and wish I had just relaxed knowing he would eventually sort it out himself.
I'm afraid I can't offer any advice as to how to make it stop but I can assure you that no, your son is definitely not abnormal and that, thoough it may feel like it's an ongoing long term problem, one day within the next few months you'll sudden'y realise that he hasn't been doing it nearly as much and shortly afer it'll stop all together.
Good luck with putting up with it in the mean time!