A composing stick is a hand instrument into which a compositor places the letters to be set up. Each row or line of letters is pushed home and held in place by a movable “setting rule,” against which the thumb presses. When a stick is full, the matter set up is transferred to a “galley” (q.v.), and from the galley it is transferred to the “chase” (q.v.). Called a stick because the compositor sticks the letters into it.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894