Clemenson was born and raised in Humboldt, Iowa, the son of drug store owners Ruth Alzora (Dayton) and Ernest Arnold Clemenson. In his early teens, he delivered the Des Moines Register, which had a long tradition of awarding scholarships to top east-coast preparatory schools to a select few "paper boys." Clemenson, a straight-A junior high school student, won a Register scholarship to Phillips Academy in Andover, Massachusetts. In 1973, while Chris was enrolled at Phillips Academy, his father died at age 58. He participated in many theatrical productions at Phillips Academy.

Upon graduation from Phillips in 1976, he entered Harvard College. From his freshman year onward he received important roles in campus stage productions. When Clemenson starred in a Harvard Lampoon Sketch comedy show, a Harvard Crimson theatre critic described Clemenson as "hugely talented actor who can trigger hysteria with any of a dozen subtle expressions or inflections." Other Crimson critics described his performances in Shakespeare plays as "a tour de force of sheer talent and intelligence" (in The Winter's Tale) and "a very fine and subtle performance" (in Measure for Measure). He displayed early on his remarkable range when he undertook with inimitable flair and hilarious effect the hugely solemn role of Erde "the green-faced torso", goddess of the Earth, in Peter Sellers's Loeb Drama Center production of "Wagner's Ring" (1979).

After graduating from Harvard College in 1980 and the Yale School of Drama in 1984, he moved to Los Angeles.

In 1999, Clemenson appeared in the Buffy the Vampire Slayer episode "Bad Girls" as a grotesquely obese demon named Balthazar. He wore a large padded suit and extensive make-up for the role, and the character's repulsive, villainous nature contradicted many of his earlier roles.

Recently, Clemenson has become known for his role as Jerry "Hands" Espenson on the television series Boston Legal. For playing Espenson, he won an Emmy Award for Best Guest Actor in a Drama Series in 2006 and was nominated for the same award in 2007. He remained with the series through to its finale in 2008.

In 2009, Clemenson joined CSI: Miami as the new medical examiner, Dr. Tom Loman. He appeared throughout the show's eighth, ninth and tenth seasons as a recurring character. 2013, also he appeared as a guest star in Harry's Law.

In film, he starred as real-life 9/11 victim Tom Burnett in United 93. On television, he was a regular on The Adventures of Brisco County, Jr. playing the part of Socrates Poole. He also had a recurring role on Veronica Mars as Abel Koontz. In total, Clemenson appeared in three episodes of the show: "Like a Virgin", "Mars vs. Mars", and "Rat Saw God". Clemenson also has appeared in a season 6 episode of NCIS, "Dead Reckoning". He also appeared in two season 2 episodes of The Mentalist. He also played Jimmy Masterson on the 3rd episode of Memphis Beat, "Love Me Tender."

In 2016, he played Deputy District Attorney william Hodgman in American Crime Story: The People v. O. J. Simpson.