Everett attended Purdue University and was selected in the first round of the 1986 NFL Draft. He was selected as the third pick in the first round by the Houston Oilers, and was the first quarterback taken that year. Unable to work out a contract agreement with Everett, the Oilers traded his rights to the Los Angeles Rams, with whom Everett played from 1986 to 1993. He then played with the New Orleans Saints from 1994 to 1996 and ended his career with a stint with the San Diego Chargers in 1997.
Purdue University recruited Everett out of Eldorado High School in Albuquerque, New Mexico, which he led, in the 1980 season, to the school's only state championship. In addition to quarterbacking the team, he also played defense as a safety.
Recruited to play either safety or quarterback, he was soon slotted into the quarterback role where he narrowly missed out on being a four-year starter at Purdue, as a game day decision before his first game as a freshman led to Scott Campbell getting the nod over Everett. Campbell held off Everett for three years, one of which Everett was able to redshirt to gain an extra year of eligibility. Upon Campbell's graduation to a seven-year career in the NFL, Everett took over the reins of the pass-oriented Boilermaker offense.
As a junior, Everett led the Boilermakers to the 1984 Peach Bowl, where he passed for 253 yards and three touchdowns. Purdue lost the game to Virginia, quarterbacked by future Green Bay Packer Don Majkowski, 27–24. Everett is also the only Purdue quarterback to ever beat Michigan, Notre Dame, and Ohio State all in the same season.
During the 1985 season, Everett led the NCAA in total offense (3,589 yards), which at the time was a school record (since broken by fellow Purdue alum Drew Brees). He finished sixth in balloting for the 1985 Heisman Trophy.
Everett earned regular membership on the Distinguished Students list at Purdue, and graduated with a degree in industrial management. During his time at Purdue, Everett regularly tutored fellow Purdue athletes in courses such as calculus and statistical analysis. He was also initiated into the Sigma Chi fraternity during his time as an undergraduate. During his senior year, he was awarded the Big Ten Medal of Honor in recognition of his athletic and academic achievements.1984: 3,256 yards with 18 TD vs 16 INT in 11 games.
1985: 3,651 yards with 23 TD vs 11 INT in 11 games.
Everett had a productive NFL career, especially with the Rams, where he was a statistical leader in several passing categories. His Rams teams were successful early in his career, earning playoff berths in 1986, 1988, and 1989, despite never reaching the Super Bowl. However, he continued to produce fine statistics, and was rewarded with a trip to the 1991 Pro Bowl game, played in Honolulu, Hawaii.
The 1993 season was a low point in Everett's career. He played in only ten games but managed to throw twelve interceptions. He only threw eight touchdown passes, tying the lowest yearly total of his career and matching his rookie total when he only played in six games. The next season in New Orleans he turned his performance around. In three years with the Saints, he threw 22, 26, and 12 touchdowns.
Over his career, Everett managed to perform well enough to be among league leaders in several passing categories. His 203 touchdown passes rank 25th all-time, and his 34,837 passing yards are good enough for 14th all-time. He also ranks 15th all-time in completions and 16th all-time in pass attempts. On a year-to-year basis, he was among the top ten league leaders in the following categories: pass attempts (seven times), completions (eight times), pass yards (seven times), and passing touchdowns (six, including leading the league twice).
Following the 1989 regular season, Everett was reportedly "shellshocked" from the numerous times he was sacked and hit in the NFC Championship Game against the San Francisco 49ers (the 49ers won, 30–3). At one point in the game, Everett was so rattled that he collapsed to the ground in the pocket in anticipation of a sack, even though the 49ers' defensive players actually had not yet reached him – a play now known as Everett's "Phantom Sack".
His struggle eventually led to a confrontation in 1994 with then-Talk2 host Jim Rome. Rome had regularly mocked Everett's aversion to taking hits on the field, mockingly referring to him as "Chris" Everett (a reference to female tennis player Chris Evert). When Everett appeared as a guest on Talk2, Rome wasted no time, applying the insult twice within the show's first 30 seconds. Everett warned Rome not to do so again, implying that physical confrontation would ensue otherwise. When Rome did, Everett overturned the table between them and shoved Rome to the floor while still on the air. Their confrontation resulted in no legal action.
In a 2012 interview with Deadspin, Everett stated that "a large burger franchise" wanted to use the footage in an ad. Everett agreed, but Rome did not, blocking the deal.
After his NFL career ended, Everett settled in southern California. He received an MBA degree from Pepperdine University and started his own asset management business.