It's a Mohan Veena. That's the bastard child of a guitar and a sitar. Actually, in this case, it's a very nice instrument, played by Harry Manx, a Canadian who plays...the blues.
The Mohan Veena looks like an arch-top guitar with lots of extra tuners down the side of the neck. It has twenty strings, and - according to Harry - only takes three hours to tune. It was invented by VM Bhatt, and I gather that it's not currently made commercially in quantity (some guy hand builds them in India), though on his website FAQ, Harry also reports that a company is making an "imitation" of the Mohan Veena you can find on eBay. He gives these imitations mixed reviews.
I just did a search on eBay and found such a listing for $745. It also said that it has 19 strings (Harry said 20 at the show) and they are giving away a copy of Harry's CD with the instrument too!
I saw Harry playing this instrument (a real one) at Club Passim last week. It was a great show, and the instrument was very interesting (I'll write up a bit more about the show shortly.)
Photo from an eBay ad