David Fox upended the legal industry once before. He hopes to do it again. The longtime dealmaker is credited with devising the playbook that helped make Kirkland & Ellis the biggest law firm in the world. His new pursuit could one day put him in competition with Kirkland and its peers.

Fox, 68, co-founded a software company, Irving Technology, that is powering a newly launched law firm, called Irving, which employs only a handful of lawyers and primarily relies on artificial intelligence.

"I hope I have one more revolution left in me," Fox said in an interview. The new firm represents a bet that AI can handle much of the routine work traditionally done by armies of associates at traditional firms.