It's what Basenjis have done for some 6000 years !
These are hunting hounds and hunting is hot wired into their DNA.
All mine have hunted, killed rabbits, squirrels, pheasant, and, in a neighbouring chicken feed store, rats. If I find them here in the garden for example, I do try to take the carcass away.
Interestingly, a rabbit's head is always the first thing on the menu. I used to find headless carcasses in the shrubbery from time to time when Ziggy and her daughter, Hope, were alive. Ziggy caught birds too, as they flew out of the hedgerows. She was so quick.
One of mine, living with an older Basenji, would catch rabbits and pheasants and drag them across the fields and lay them beside the old girl when she could no longer hunt. Owners found this very touching but could have done without all the fleas she brought into the house.
So far Mku's tally is two squirrels. But he didn't eat either of them. Not much meat on a squirrel.
If you don't want them to hunt, I suppose you have to keep them tethered. But this behaviour is to be expected in a hunting hound.