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Chag sameach means "Happy holiday" in Hebrew. Chag is the Hebrew word for holiday, sameach is the Hebrew word for happy. Chag sameach is the traditional greeting among Jews before any holiday.
"Merry Christmas" Chag Molad Sameach חג מולד שמח Chag basically means holiday or "festival." Molad generally means "birth." And Sameach basically means "happy." Thus the literal translation...