Botox for Depressor Labii Inferioris to Control Chin Movement?

This off-label use of Botox should be done by an experienced Botox injector physician. A very low number of units should be injected, about one or two the most, per insertion, until the desired result is obtained. The physician should examine you by visualization as well as by palpating the chin and feeling the muscle movement as you smile to determine the origin of the involved muscle This will help determine the best placement for the Botox. Keep in mind that there could be an unwanted result such as lowering of the lower lip, drooling, difficulties with speech and playing a wind instrument. Should an undesired side effect occur, it could last three to four months before it resolves spontaneously.

Dear Schmoopy
Sure BOTOX is used to control the depressor anguli oris muscle. However, a far better approach is to fill these regions instead with hyaluronic acid fillers. Generally, the appreance of much this over activity is due to a loss volume. FIllers allow this to be addressed without a risk to the shape or function of the mouth.

Simple answer = YES! But hard to achieve. You need to use a VERY experienced injector, taking they time and maybe multiple weekly visits to get the desired result. 
Best of Luck!