Eating Chinese food in the 1920s and the 1930s, when many Jewish people immigrated to the US, was a new and sophisticated thing to do. Over time many Chinese food dishes has become dairy-free. That makes Chinese food kosher-ish. Chinese restaurant owners, unlike some restaurant owners, didn't discriminate; you could be a space alien and they wouldn't care. Plus, everything in town was shut for the holiday but Chinese restaurants were open. That would narrow down your choices when you decided to go out for a bite.
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Why Eating Chinese Food on Christmas Is a Sacred Tradition for American Jews