Kentucky State Police Trooper Tony Watts said the shooting happened around 11:30 a.m. Friday at Ben's Quick Stop in Hazard, a rural town more than 100 miles southeast of Lexington.
Noble said Neace, whose duties were like that of a city council member but on the county level, was active in the community and was in his second term.
His brother, Don Neace, told the Lexington Herald Leader that he can't understand why anyone would want to kill him.
"It just doesn't make sense," Don Neace said.
A woman who answered the phone at the convenience store would not discuss the shooting.