I read this from the web. It seems to be a good idea:
http://redbus2us.com/h1b-issue-at-immigration-checkpoint-within-us-must-carry-passport-visa-for-travel/
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GC holders are required by law to carry their GC at all times with them ( though very few ppl follow that out of fear of losing wallet ( or if they get robbed ) . I am one of them. I always carry a photocopy of GC in my wallet ). since its a hassle to order replacement GC from USCIS in case if you lose it.
