A Basenji will ALWAYS be looking for a way to run, run, run! They are hunters and the least chance to chase something will completely take them over, regardless of their training. Yes, keep them always on a leash, unless the fencing you are talking about is high, deep in the ground so they can't dig under it, and chain link is not a great idea because they will climb it - they also jump pretty high with the right motivation, like a squirrel, a rabbit, a bug, a butterfly, the wind blowing in that direction, a noise in the next county, etc., etc.. Also be really careful when you leave the house, a they will slip through your legs and be gone before you can react. This one I know from experience, and I about killed my old legs chasing her - thank God she unknowingly ran into a dead end corner where I could grab her up before she charged me trying to get past.