From the AA Timeline:
Dr. Bob lapses into drinking again but quickly recovers. The day widely known as the date of Dr. Bob’s last drink, June 10, 1935, is celebrated as the founding date of Alcoholics Anonymous. Dr. Bob and Bill spend hours working out the best approach to alcoholics, a group known to be averse to taking directions. Realizing that thinking of sobriety for a day at a time makes it seem more achievable than facing a lifetime of struggle, they hit on the twenty-four hour concept.