Song Facts:

Courtesy of Songfacts

This song takes us inside the head of a deranged murderer. It started when lead singer David Byrne decided to write something in the vein of Alice Cooper, whose shock rock was all the rage. Byrne started with the first verse, which establishes a dangerous paranoia:

I can’t seem to face up to the facts
I’m tense and nervous and I can’t relax
I can’t sleep ’cause my bed’s on fire
Don’t touch me I’m a real live wire

The rest of the lyric is even more capricious, with this guy admitting he’s a psycho killer and warning us to run. It ended up being far more introspective than most Alice Cooper songs, but just as believable: while Cooper is a completely different guy off stage (Vince Furnier), Byrne really is the socially awkward genius he portrays in performance. He’s never killed anyone (that we know of) but can convincingly inhabit the character.
This was the first Talking Heads song. It was written in 1973 at the Rhode Island School of Design (RISD), where David Byrne and drummer Chris Frantz had a band called The Artistics. When Byrne presented the song, he explained that he wanted a Japanese section in the bridge, but when he asked a girl who spoke the language to come up with some murderous words, she understandably freaked out. Frantz’ girlfriend, Tina Weymouth, spoke French, so they had her write a French part for the bridge instead. She drew inspiration from the Norman Bates character in the 1960 Alfred Hitchcock thriller Psycho, which influenced the next verse:

You start a conversation you can’t even finish it
You’re talking a lot, but you’re not saying anything
When I have nothing to say, my lips are sealed
Say something once, why say it again?

Byrne incorporated a French line into the chorus: “Qu’est-ce que c’est?” (meaning “What is this?”) and followed it with a stuttering warning:

Fa-fa-fa-fa-fa-fa-fa-fa-fa-far better
Run, run, run, run, run, run, run away

The end result is one of the most famous songs about a psychopathic murderer, influenced by two touchstones of the genre: Alice Cooper and the movie Psycho.
The French section in the Bridge roughly translates to:

What I did that night
What she said that night
Realizing my hopes
I launch myself towards a glorious destiny

This reveals that the psycho killer is targeting a woman, just as Norman Bates did in Psycho.
David Byrne and Chris Frantz played this a few times in 1974 with their band The Artistics. Later that year, after Frantz and Tina Weymouth graduated from RISD (with degrees in painting), they moved in together with Byrne in a slummy apartment in New York City. Tina became their bass player, and they called their new group the Talking Heads. Starting in May 1975, they got some gigs at the club CBGB opening for the Ramones. “Psycho Killer” and a few other originals, including “Warning Sign” and “Love Goes to Building on Fire,” were in their setlist, rounded out with covers like “96 Tears.” They got the attention of various record labels and eventually signed to Sire Records. After adding guitarist Jerry Harrison to the group, they released their debut album, Talking Heads: 77, in 1977. Released as a single, “Psycho Killer” was their first chart hit, reaching #92 in March 1978.
Credited to David Byrne, Chris Frantz and Tina Weymouth, this is the only song on the Talking Heads’ debut album that isn’t listed as a solo Byrne composition. Songwriting credits quickly became a sticking point in the band as Byrne became the focal point and gave the impression that he did all the songwriting himself. Frantz claims that he wrote the second verse to “Psycho Killer,” but Byrne has downplayed his contribution to the song, telling Mojo, “Chris and Tina helped me with some of the French stuff.”