The story
From chin + up, but not a deverbal, unlike pull-up. The chin-up and the muscle-up as variations of pulling oneself upward were named later than the pull-up, with influence from its name.
Etymology from Wiktionary, CC BY-SA 4.0.
chin-up
Today it means: An exercise done for strengthening the arms and back, in which one lifts one's own weight while hanging from a bar. It can be defined more restrictively on criteria like the arms starting at lock-out, or the chin requiring contact with the bottom of the bar, or touching the neck to the bar. Palms may be facing in any direction. Full definition →