Chase Manhattan Bank, the nation's third largest, boosted its prime rate to 16 1/4 percent from 15 1/2 percent. No. 2 Citibank, No. 5 Morgan Guaranty, and No. 6 Chemical quickly followed Chase's move, and other major banks were expected to do so. Most analysts had anticipated an increase in the prime -- the rate charged the most creditworthy corporate customers -- after money-tightening moves Friday by the Federal Reserve Board.