Shimano MTB and Road Components Compatibility
You need a 10 speed chain. You can buy one from Shimano, SRAM or KMC. There isn't a compatibility issue between different Shimano/SRAM Mountain/road drivetrains in regards to the chain. The only 10 speed chain on the market you can't get are ones marked for Campagnolo (*).  

I'd prefer an SRAM one (e.g. PC-1051) or KMC one (any 10 speed chain that is marked Shimano/SRAM compatible, which is pretty much all they sell) because they use a special link, rather than a special rivet like Shimano (which is annoying, at best). The SRAM link is one time use, but the KMC one can be disconnected multiple times. 

(*) Well, depending on who you ask, it will work; I don't know anyone who would actually run that situation. Plus, there are 2 varieties of 10 speed chains for Campy as well.