'Chestnut' is an idiom referring to a familiar tune or argument: 'We've all heard that old chestnut.'
Tea dance - Wikipedia, the free encyclopedia). The other boys (hence the repeated mention of 'the gang') are envious (the lyric says 'jealous', but it means 'envious'*).
PS *A lot of people would be tolerant of this abuse of 'jealous'; some would even say there's nothing to be tolerant of, and the meaning has just widened. But I think it's a useful distinction, and try to preserve it.
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