Just guessing wordwind, but Chamber's is dictionary publisher, --the english equivient to our Websters.. in the UK if you told some one "chamber's said".. it would be about the same as saying "Webster's said" most everyone would realize you were talking about Websters Dictionary.
(if i am not mistaken, at one point even Sherlock Holmes checks a word or term in Chamber's..) Just as Oxford guides have a reputations, (and you might want to own an "Oxfords guide to English Usage", (and wouldn't really care who actually published it,since it would be under the imprimater of Oxfords,)* I think the book in question is printed under the imprimater of Chambers.
*of course this a bad example, since Oxford University has its own "press" or publishing house.
