As a redshirt freshman in 1987, he was the Cougars third-string tight end and played on special teams as well. In 1988, as a redshirt sophomore, he recorded nine receptions for 121 yards and one touchdown. As a redshirt junior in 1989, he was named the team's starting tight end and started all 13 games. He was named First-team All-American by The Sporting News, a Third-team All-American by the Associated Press and First-team All-Western Athletic Conference.[4][5] He was also featured in an article in Sports Illustrated as a junior who would e turning professional a year early. In 1990, as a redshirt senior, he was a consensus All-American.[4] He recorded 68 passes for 1,156 yards (an NCAA record for tight ends) and two touchdowns. He finished fifth in the nation in receiving yards.[3] His record stood until 2005 when it was broken by Tulsa's Garrett Mills.[6]
In 2011, Smith was ranked the third best tight end in BYU history by the Deseret News,[7] and then in 2015, he was ranked the 27th best football player in school history.[8]
Prior to the NFL Draft, Smith attended the NFL Scouting Combine and recorded a 5.05 in the 40-yard dash due to multiple injuries.[2] After which a Sports Illustrated article was published before the draft that included negative quotes. The magazine featured tight end Jerry Evans, who was at the Combine and said of Smith: "He's effeminate. He can't block." NFL scout Dave Te' Thomas added: "I think Chris will look good in a business suit."[2]
Smith is the son of Robert and Kay Smith.[2] He is one of 10 children.[2] His older brother, Ken, also played for the BYU Cougars as a starting nose guard.[2] Before playing college football, Smith served a mission to Albuquerque, New Mexico from 1985–1987. He married Sarah Newby in April 1989,[3] the couple have three children.[2]