Referencing references within a quote
Chain referencing is not required unless you reference some information from the chain reference that is more than what is already referenced within the first citation. 

To add clarity, if you want to cite a matter from [A] which is cited as a quote from [B], then citing [B] would be appropriate. Otherwise if [A] adds some insights to [B], then citing just [A] would be fine. If in addition to this you derive some insights from [B] which is not noted in [A], then you must cite both [A] and [B].