My Basenji is also obsessed with chasing squirrels (and cats). I've tried reprimanding her (that works for about 3 seconds), but her attention still stays focused on the prey at hand…LOL What I recently started doing, when she sees the squirrel and goes into chasing mode, I turn the opposite direction and start running with her until we are far enough away from the squirrel that she no longer cares about it. she starts enjoying her run with me so much that she forgets about it.
laugh Mine apparently JUST figured out she can do that this last weekend. I was so impressed.
I think as long as your Basenji can get down safely, and isn't going to be tempted to hop over any fences… why not?
Now if they actually catch one, just hope they don't bring it inside…