What causes this deep chin crease and how can I fix it? (Photo)

If I am getting your question right, you are mentioning 'labiomental groove'.
this groove is defined as a groove between lower lip and chin.
There are several causes for deep labiomental groove.
Sometimes it is caused by micrognathia, and malocclusion ( your overbite may be one cause.)
In some cases it is caused by hypertrophy of chin bone, or hypertrophied muscles.
To define the definite cause, you should visit your surgeon.

It is a widely spread idea osseous genioplasties consist of only
sliding genioplasties, which is absolutely untrue; with just sliding the
chin bone you can address successfully the issues and wises of no more
than 30% of the patients seeking chin surgery.
There come the
multidimensional osseous genioplasties, those aiming to modify
structurally the chin bone by means of increasing or decreasing the
dimensions of one, two or three dimensions of the chin. 
Actually
there can exist weird combinations in which the case needs shortening
certain axis and enlarging other/s. You are one of such peculiar,
challenging and (professionally) interesting cases.
Your atypical facial profile at the chin and the deep labiomental crease is due to a combination of the following:
-extremely short vertically chin dimension
-too prominent and oversized anterior chin projection
-(I guess, frontal and oblique views needed) too broad and square horizontal width
Therefore
you'd be a case for vertical enlargement (bone graft supply is bound
here) and anterior deprojection / reduction (never ever sliding
backwards, which leads to a double chin deformity) and eventually
horizontal narrowing.
Eventually we can consider a strip grafting to smooth the labiomental crease, but it is very likely with just the aforementioned custom genioplasty may suffice; intraop assessment and decision-making is bound here. You may wonder about the effect of only correcting the depth of the labiomental creas... in your case a total disaster, an "en bloc" look and too masculine.
Feel free to request additional information and advice, with full set of images if possible.