"CHALMERS, Chambers. The correct forms are Chalmer and Chamber, from Old French, de la chambre of the chamber: (1) a chamber attendant, (2) of the Treasury chamber (camera) , and so metonymic for CHAMBERLAIN, q.v. The spellings with the 's' are later. When the Old French word was naturalised in Scots it lost b by elision, and received l to safeguard as it were, the length of the preceding vowel..."
from The Surnames of Scotland - George F. Black 1946 The New York Public Library