If the grinding occurs only when you are on the middle ring, this points to the middle ring being worn (look for "hooked" teeth), and it is especially likely with a new chain. The old worn chain probably mated fine with the worn ring. I suspect that the middle ring was most used and got the most wear, which is why it's "protesting" the new chain while the inner and outer rings are not giving you problems. Replace the middle ring and the problem should resolve. BTW, your rear sprockets are probably worn too, but not so much that they don't "cooperate" with your new chain...yet.
You might need to replace the rear hub gears.