Shimano Sis Bar-end Shifters on a Shimano Deore xt derailleur
It depends on which generation of XT derailer and how many speeds your cassette is.

For the last generation of 9spd and earlier (RD-M772 and lesser numbers), the actuation ratio is all the same for mountain and road. So you would use SL-BS77 shifters with a 9 speed cassette, SL-BS64 for 8, etc, and the shifters won't care which derailleur they're attached to. 

Shimano changed their MTB RD actuation ratio when they introduced 10-speed mountain components, and this is where the answer gets more complex. If you're using any 10-speed Shimano RD, the only choice I know of for bar end shifters (unless you use a pull adapter) are the ones made by Microshift specifically for this purpose. Road/tri bar ends such as SL-BS78 will not work because they're for the older actuation ratio. And if you're using a 10-speed XT derailer, you must use a 10-speed cassette.

Same deal for 11. If you have the 11-speed XT derailer RD-M8000, the only bar end shifter choice (again that I know of) is the one made by Microshift.

Use whatever chain your cassette is made to take.