A group controlled by a Republican state senator is backing Honolulu lawyer John Carroll, the underfunded rival for the GOP gubernatorial nomination to Lt. Gov. James “Duke” Aiona.

Paychecks Hawaii, a political action committee linked to Smart Business Hawaii, endorsed Carroll on Wednesday.

The chairman of Smart Business Hawaii is Sen. Sam Slom of the Diamond Head and Hawaii Kai areas.

Carroll is considered a pronounced underdog to Aiona, who has raised more money and is backed by GOP Gov. Linda Lingle and the Republican Governors Association.

Slom also is supporting Honolulu attorney Adrienne King for the GOP nomination for lieutenant governor over Rep. Lynn Finnegan of Mapunapuna.