Precinct 5 Constable Brad Miers also was leading in his bid for re-election.
Nutt was running for a second term. Chaney, who already has served 24 years, was seeking a seventh term.
Complete, unofficial returns showed Nutt, a Republican, with 20,941 votes, or 77.37 percent of the votes cast for sheriff. Challenger Bill Burton, a Democrat, had 6,126 votes, or 22.63 percent, according to unofficial returns.
In the race for tax assessor-collector, Chaney, who switched from the Democratic Party to the Republican Party, was opposed by Bryan Barker, a Democrat.
With all 27 precincts reporting, Chaney had 21,799 votes, or 80.32 percent, to Barker’s 5,340 votes, or 19.68 percent.
In seeking a new term, Nutt said the sheriff’s office has become more professional under his leadership and a more aggressive, proactive law enforcement agency. He said the sheriff’s office has made hundreds of narcotics cases and saved the county money through various measures while obtaining grants for improvements.
Nutt defeated Burton, now employed as a police officer for Trinity Valley Community College.
Chaney handily turned aside a challenge from Bar-ker, a former corrections officer now disabled who was making his first bid for public office.
Henderson County voters in Precinct 1 also were picking a new commissioner to succeed Joe Hall, who did not seek re-election.
Scotty Thomas, a Republican, battled David McClaun, a Democrat, for the position, with unofficial vote tallies showing Thomas in the lead.
Thomas had 4,795 votes, or 75.70 percent of the total votes cast for Precinct 1 commissioner, and McClaun received 1,539 votes, or 24.30 percent, according to the complete, unofficial election returns.
Precinct 5 voters also voted on a constable. They picked between the incumbent, Miers, a Republican, and challenger Rick Simmons, a Democrat.
Complete, unofficial returns showed Miers garnered 4,035 votes, or 75.62 percent, to Simmons’ 1,301 votes, or 24.38 percent.