Mixing 9-speed Tiagra and 9-speed Deore XT I currently have a road bike with the following setup for the gears:

9-speed Tiagra front and rear derailleurs, Sora shifters, all from 2009:
30/39/52 Crankset
11-25 Cassette.

I need some more low gears for hilly areas, and I am thinking of switching to a 9-speed Deore XT derailleur and 11-32 cassette. Is it possible / compatible? Do you think that cross-chaining would be an issue? Will I need a new chain?
Yes, that will work just fine. I have a similar setup on my touring bike, Tiagra shifters and an LX derailleur.