Good lord. You'd think that being on the lookout for a relatively rare breed would mean relatively few hits scored. But alas. This kid is in the LA City shelter in the East Valley Animal Care and Control center. I have no idea about size, mix, temperament or anything, but the city shelter doesn't usually classify a dog as a basenji mix unless it either a) looks very much like a B, or b) yodels. If you're in the area, check her out. She's about 9 months old. Medfly Basenji Rescue is, sadly, full to bursting with dogs in trouble.
Her ID is: A1048471
Here's her PetFinder ad: http://www.petfinder.com/petnote/displaypet.cgi?petid=14237781