WASHINGTON (Reuters) - Rand Paul, a favorite of conservative "Tea Party" groups, beat the establishment choice on Tuesday to win the Republican U.S. Senate primary in the biggest victory so far for the loosely organized movement, CNN projected.

Paul, a doctor and son of libertarian Republican Representative Ron Paul, beat Secretary of State Trey Grayson in a race seen as an early test of the strength of the Tea Party.

Grayson was the handpicked choice of Senate Republican leader Mitch McConnell. Paul will face whoever emerges from a field of five Democratic candidates in the November election to replace retiring Republican Senator Jim Bunning.

(Editing by Will Dunham)