Thank you all for the suggestions. This is just what I was looking for, "but she could learn to leave the chickens alone while you are out enjoying the yard together."
We have another yard where she goes normally, but we just fenced in the backyard so we could have the dogs join us.
Our cats have their own indoor room, and we built an outdoor playroom that is completely basenji-proof.
The chickens are a new addition, and they have a secure house, but I don't want Lula getting injured trying to figure out a way to get into the hen house. And, unfortunately if she gets past people coming in and out of the house, our neighbor's fencing is not secure enough to keep out a basenji.
We had 2 basenjis before who loved to chase rabbits, but they were great with cats and never killed anything. We have been surprised by how strong Lula's prey drive is. After reading the story about the deer, I have no doubt she would try to do the same. I figured if there was any training method out there that might work on a basenji, the forum would know. She has become desensitized to one of our cats, and they spend a lof time together, however, not without supervision.
She is a beautiful dog, and for the first year was amazingly well behaved for a basenji. Once she realized her "forever" home was for real, and we were madly in love with her, she started letting her basenjiness show.
Gotta love 'em!