Hi Dave -
Without seeing you run, it’s hard to make a diagnosis but usually shin splints are caused from tight calves and/or too much tension in the front of the leg, usually caused by stiff ankles (dorsiflexion) and tension in your feet.
You say you switched from heel striking to Chi Running - did you address the posture, lean, and ankle lift? The midfoot landing comes from creating conditions for that to happen. If our only focus is not heel striking, then I suggest you go back to basics. Either re-read the book or watch the DVD, and, even better, contact a certified instructor in your area. They will be able to pick up what is going on pretty quickly.
Good luck and let us know how it goes.
Certified Chi Running and Chi Walking Instructor