early 13c., "subordinate place of worship added to or forming part of a large church or cathedral, separately dedicated and devoted to special services," from Old French chapele (12c., Modern French chapelle), from Medieval Latin capella, cappella "chapel, sanctuary for relics," literally "little cape," diminutive of Late Latin cappa "cape" (see cap (n.)).
By tradition, the name is originally in reference to the sanctuary in France in which the miraculous cape of St. Martin of Tours, patron saint of France, was preserved. (While serving Rome as a soldier deployed in Gaul, Martin cut his military coat in half to share it with a ragged beggar. That night, Martin dreamed Christ wearing the half-cloak; the half Martin kept was the relic.) The other theory is that it comes from Medieval Latin capella in a literal sense of "canopy, hood" and is a reference to the "covering" of the altar when Mass is said.
The word spread to most European languages (German Kapelle, Italian cappella, etc.). In English from 17c. it was used also of places of worship other than those of the established church.