I haven't had any aggressive dogs chase me (except for one little terrier type once, but he wasn't very threatening) but I have had dogs run after me as I run by. That's just a normal instinct. What I've done is stop, face the dog and sternly say "go home!" and if the dog doesn't begin moving in the other direction I've actually chased it back to its yard, and this has worked every time I've done it. Then I just continue on my way. I also carry pepper spray that I am prepared to use if a dog is truly aggressive (really, it's more for aggressive PEOPLE that I carry it, but it is useful in either case). That said, I'm not sure that chasing the dog is such a good idea if it is behaving aggressively.