hat box
From Longman Dictionary of Contemporary Englishhat boxˈhat box noun [countable] DFCa special box used for carrying a hat inExamples from the Corpushat box• He is holding what looks like a square brown leather hat box and a white Chanel carrier bag.• We sat facing across a desk in a rather denuded office in Carlos Lott's building which resembles an unravelling hat box.