Michael Bradley had a one-stroke lead when first-round play was suspended at the River Highlands course.
Bradley was six under with two holes left when play was stopped in the late morning.
Officials opened the driving range late in the afternoon and hoped to resume play but more rain caused another delay and officials eventually decided to call it a day. Play is to resume Friday at 7 a.m. (1100 GMT).
Fijian Vijay Singh was in a group of seven players one shot back. Singh hit his drive into the woods on the par-four 15th hole just before the rain delay. He found his ball and was expected to take a drop when play resumes.
Former Masters champion Zach Johnson was in a group at four under.