It was written by group members Annie Lennox and David A. Stewart, and appears on the duo's sixth studio album, Savage (1987).

Lyrically, Lennox sings of mustering the power to leave a destructive relationship with a lover who does not return the affection she deserves ("...a woman's just too tired to think / about the dirty old dishes in the kitchen sink").

A reviewer from Cash Box called "You Have Placed a Chill in My Heart" an "arresting, riveting record" and praised Lennox's "powerful, beefy [vocal] performance.

"[2] David Stubbs from Melody Maker said, "Dotted with Lennox's dramatically inept, watery squeals, like those of an orgasmic weasel, this is an electro-pop song about love, which, we are told, is pure, blind, hot and cold.

"[3] Pan-European magazine Music & Media wrote, "Another spellbinding song from the beautiful Savage LP.