I've read a few pointers,
The tighter the setting/arena for the chase, the more tension it can maintain. It should be defined in some way.
The chase scene should be about the chase, not the characters.
My own thoughts, I haven't written any that I've gone back and polished, but these are general rules:
Write in terms of action, reaction, like always.
a 1. They see pursuer peek around some columns.
r 2. They run faster.
a 3. They almost run into a cart filled with hay.
r 4. Dump the hay and make a break for another alley.
a 5. One chased guy stops to breath.
r 6. The other man, having to wait for him, curses and says they have to move.
a 7. Another pursuer, maybe the same, maybe not, calls out for them to stop.
r 8. The tired man lumbers around the corner.
a 9. The not tired guy comes up to a low, open window.
r 10. They duck inside.
a 11. They hear the pursuer pass by.
r 12. They stay very still, eyes wide.
a 13. They hear the other guys, from the hay cart pass.
r 14. They go out the front door and double back around, off to their destination.
Just put yourself in ancient Rome and run around like you're chased for a while, jot down what comes to mind lol.