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It doesn't strike us as an ideal time to be launching a splashy new hotel in Midtown, but turbaned hotelier/playboy Vikram Chatwal's latest property opened today on West 47th Street. Chatwal gave the property the gimmicky name Stay. But it might just work out to his advantage: In this economy, you can interpret it as Chatwal's personal request that you stay at his hotel and stay there for a very long time. [, HotelChatter]