Thumb-Sucker

Our son J (almost 3 1/2 yrs old) has sucked his thumb since birth, and after his dentist cleaning/visit today, I'm inspired to start breaking him of this habit. He sucks his right thumb mostly to fall asleep at nap- and night-times. He usually wakes up not sucking his thumb so I know it's just a "falling asleep comfort" ritual. If you have any tips or tricks that worked for you, I'd love to hear them!