you could use lukewarm water with cotton wool or diluted hibiscrub from the vets. i wouldn't use conditioner, you'll never get it out properly. is he in with your other chin? if he is, the other chin may give it a go and groom that bit although that can take time.
i would double check what's matting the fur, it could be he has a little wound that's seeping. i just got a rescue chin and she had a bit of dried up gunk under her chin so i checked it out and she has a incisor root growing through her chin that's causing an abscess as well..
worth making sure he just dipped it into something!