Green’s Dictionary of Slang

chief muck of the crib n.

[muck is synon. with both high muck-a-muck n. and Lord Muck under muck n.1 but predates both and must thus be a fig. use of colloq. muck, anything filthy, disgusting or abhorrent + crib n.1 (1)]

an important person, but within only a small field of activity.

[UK]‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 49: Chief muck of the crib—literally, principal lump of dirt; but, freely, meant to designate a head director in small affairs, and cannot possibly mean the Governor of the Bank of England, the Lord President of the Council, &c. since every one knows that crib implies a single place, as a tap-room, a drinking-booth, coffee-shop, &c. Yet some there are who perversely extend the term to the first gentleman of England, and call that the crib where he presides when Parliament is opened or shut ― and he ‘Chief,’ &c.