Childress entered NASCAR competition in 1969 during a drivers' strike at Talladega Superspeedway, when NASCAR president Bill France Sr. sought replacement drivers. By 1971 he was racing as an independent driver under the No. 96, later switching to No. 3 in 1976 as a tribute to fellow driver Junior Johnson. Though he never won a points race as a driver, Childress established a reputation for consistency over a decade of competition. He recorded six top-five finishes, 76 top-ten finishes, and five top-ten points season finishes, with a career-best standing of fifth place in 1975. His single win came in the unofficial invitational Metrolina 200 in 1974.
Childress retired from driving in 1981 after Rod Osterlund sold his team to Jim Stacy, and Osterlund's driver Dale Earnhardt chose not to continue with the new ownership. On the recommendation of R. J. Reynolds Tobacco Company, Childress retired from competition and installed Earnhardt in the No. 3 car. That first pairing lasted a single season. Ricky Rudd drove for the team in 1982 and 1983, delivering RCR's first Cup victory at Riverside in June 1983. Earnhardt returned for the 1984 season.
The Earnhardt and Childress combination became the most successful driver-owner partnership of the 1980s and 1990s. Together they won six NASCAR Winston Cup championships: 1986, 1987, 1990, 1991, 1993, and 1994. In the process, RCR also claimed its first Owner's Championship in 1986.
When Earnhardt was killed during the final lap of the 2001 Daytona 500, Childress promoted his Busch Series driver Kevin Harvick to fill the vacated No. 29 car. Harvick won in his third Cup start at Atlanta Motor Speedway. Childress subsequently expanded RCR into a multi-car operation. Harvick won the Busch Series championships in 2001 and 2006, making RCR the first team in NASCAR history to have claimed championships in all three of the sport's national series, predating Hendrick Motorsports' achievement of the same feat.
Further series titles followed. RCR won the Busch Grand National Series Owner's Championship in 2003 (with Kevin Harvick and Johnny Sauter) and in 2007 (with Scott Wimmer and Jeff Burton). The team claimed the NASCAR Camping World Truck Series championship in 2011 and the NASCAR Nationwide Series championship in 2013, both with Childress's grandson Austin Dillon driving the No. 3 — the first time the number had been used full-time in a national series since Earnhardt's death.
In June 2011, Childress was involved in a physical altercation with driver Kyle Busch in the garage area following a Camping World Truck Series race at the Kentucky Speedway. NASCAR fined Childress $150,000 and placed him on probation through the end of the 2011 season. More than a decade later, in September 2022, the two parties announced that Busch would drive RCR's No. 8 Chevrolet in the 2023 Cup season; Childress presented Busch with a Rolex watch at the signing as a reference to the confrontation.
In the 2010 Sylvania 300, RCR driver Clint Bowyer's winning car failed technical inspection twice. NASCAR penalised the team with a six-week crew chief suspension, a 150-point deduction, and a $150,000 fine. On appeal, the suspension was reduced to four races and the fine to $100,000, though the points deduction was upheld. In 2015, NASCAR penalised the team's No. 31 car driven by Ryan Newman for alleged tyre deflation, resulting in further fines and suspensions.
Childress married Judy, and together they established the Childress Institute for Pediatric Trauma in 2008, focused on reducing death and disability from injuries to children. He opened a vineyard in the Yadkin Valley near Lexington, North Carolina in 2004. Since 2022, he has been co-owner of the Carolina Cowboys bull riding team in the Professional Bull Riders Team Series; the team won the 2025 PBR Team Series Championship. He served on the board of directors of the National Rifle Association until 2019.
Childress was inducted into the Motorsports Hall of Fame of America in 2016.