I have a fascia board that slopes into a stucco chimney wall. Water runs on the board and then drips onto the chimney -- what's a good way to prevent this ? There's no gutter on that board since this is not a horizontal surface.

How about a picture, we can only guess as to what your exact situation is.

How about a picture, we can only guess as to what your exact situation is.

Attached is a diagram showing the spot in question.

How much shingle overhang do you have? I'd put a small roof diverter a couple of inches above the end of the fascia.

There's actually already flashing on the chimney that diverts the water back and around the chimney. So the only remaining water is what's getting on the fascia between the roof top and the end of the board and leaks down.

That's why I asked about shingle overhang. You should have 1-1.5 inches of shingle over the fascia edge. Otherwise, there is not much to do.