Most basenjis will chase anything that moves! Lure coursing events are held by AKC and ASFA for sighthounds only. Dogs chase a white plastic bag lure around courses (typically 600 yards and over) with up to 3 other dogs of its own breed. Also, there is a singles class where your dog can run by him/herself.
There are no prerequsites if you run your dog in the singles competition, but in the group competition, you will need to demonstrate he/she can run with other dogs.
If you want to just run your dog for fun, visit Lure Coursing Fanatics (Southeastern Wisconsin)