[defrost]

From a brief dip in the multi volume full OED it looks like "Vice Chairman" (etc) came about via vyse | visage | "face" .. as in "This person is a substitute | deputy | "the face" of another person or role"

It's a usage going back to at least 1597 and lost in the fog of time before.

[glogla]

Interesting. It works the same in a most European languages (Vicepresidente, Vice-président, Vizepräsident, Wiceprezydent, Viceprezident, Віцепрезидент, Вице-президент, ...).