Beaufort County Sheriff's Capt. Bob Bromage told multiple media outlets that the shooting happened after 30-year-old Alvin Sosa followed 51-year-old Gary Lee Simmons and his daughter as they drove on Hilton Head Island.
Deputies say when they got to Sosa's apartment complex, Simmons and Sosa began arguing in the road and Simmons fired at least two shots with a rifle, killing Sosa.
Bromage wouldn't say what the two were arguing about or why Sosa was following Simmons.
Simmons remained in the Beaufort County jail Monday afternoon. It wasn't immediately clear if he had an attorney.