We found one dictionary that defines the word puff one's chest:

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1. puff one's chest: Wiktionary

Definitions from Wiktionary (puff one's chest) ▸ verb:  To act arrogantly and resolutely. ▸ Words similar to puff one's chest ▸ Usage examples for puff one's chest ▸ Idioms related to puff one's chest ▸ Wikipedia articles (New!) ▸ Words that often appear near puff one's chest ▸ Rhymes of puff one's chest ▸ Invented words related to puff one's chest