Definitely a quandary.
If you don't tell your boss and the new employer calls him for a reference, and this is the first time he hears about it, you could be toast.
If you approach your boss beforehand, they may make a counter offer to keep you there. So you'll need to know what your response will be ahead of time.
Personally, I've always been up front with my boss when looking for a new job. Most are understanding if the new position is a good career move for you. YMMV.
Definitely a tough situation, but sushi's advice would be what I would do.