It is a move that will be supported by many as an affirmation of the union's support of maintaining employment, but baffle others, who may see it as a waste of resources.
The union is concerned that the threatened job cuts are a growing trend in the British book and publishing industry, with "adverse knock-on effects to employment and local economies".
Ann Field, Unite/GPM national officer, said: "Unite members in other publishers, book printing and distribution companies are concerned at yet another blow being aimed at the UK book industry.
"Unite members are signing a petition calling for the retention of one of longest-established and finest English language reference works, and particularly to retain its production and publication in Edinburgh."
"Replacement of the printed word is only in the interests of accountants and bankers, not the readers and researchers. Unite is right behind the National Union of Journalists (NUJ) in its continuing campaign to save these jobs in Edinburgh."
Parent company Hachette tried to find a buyer for the Edinburgh-based business but failed. Last month, it announced plans to merge the business with its Paris and London arms.
Euro MP David Martin is to lodge an appeal with the EU to give the dictionary protected geographical status, claiming the work is an iconic brand closely identified with the Edinburgh.
Unite is the latest body to support the company – an online petition backed by Publishing Scotland has gained 650 signatures so far.
Chambers was formed in 1819 and was responsible for producing its first dictionary in 1867. It merged with reference company Harrap in the early 1990s.