Chalambaga sounds as basque, but is not rated in any of the books about basque surnames that I have, the more simmilar surnames that I have found are: Chalaeta, Chalamendi, Chalar, Chamalbide, I have look up Zalambaga, and is not rated, neither Achalambaga (Achalandabaso)

Sorry, but the only way to know more about this surname is making a godd family tree, in any case I cannot say that is not Basque, so if you discover any more about it please let me know it