Looks like it’s actually possible. Via CBC.ca:

The treatment, called low-intensity pulsed ultrasound, massages the gums to stimulate jaws, encourage growth in the roots of teeth and aid healing in dental tissue.

“If the root is broken, it can now be fixed,” said Dr. Tarak El-Bialy of the Faculty of Medicine and Dentistry. “And because we can regrow the teeth root, a patient could have his own tooth rather than foreign objects in his mouth.”

Bring it on :-)