What would I need to get done to fix the gap/indent where my chin meets my jaw? (Photo)

That area is sometimes called the pre-jowl sulcus. Intense to form in individuals who have an undersized mandible. With an undersized mandible patients also typically have an overbite dental occlusion, profile pictures that will have the upper lip giving more forward projection than the lower lip, occasional premature double chin formation and lack of jawline definition.
The easiest and best treatment is fillers in the sulcus to compensate for the apparent lack of volume.
The primary problem has nothing to do with fat distribution or soft tissues at all. The primary problem is bone structure and certain bone structures cause soft tissues to drape their face in certain manners because of the tension and pull of facial muscles and gravity.
Considering that most people are not going to undergo jaw advancement surgery soft tissue manipulation while it doesn’t treat the primary problem tends to be a second best option. For this well done placement of fillers can give pretty good results.
Obviously results are highly dependent on who does the treatment so seek out providers in your community who have talent and experience working with fillers.
Best,
Mats Hagstrom MD