Mix together the balsamic vinegar, honey, mustard, thyme, and garlic cloves in a small bowl. Set aside.
In a heavy bottomed pan over medium low heat, pour the olive oil into the pan, and season the chicken with salt and pepper. Once the oil is hot add the chicken thighs skin side down. Cook the chicken thighs for 7-10 minutes, or until the skin is deeply gold brown and easily releases from the pan. Add more oil as needed
Flip the chicken and cook on the other side until golden brown and the chicken is cooked through all the way, reaching an internal temperature of 165°F. About 10 minutes.
Pour the balsamic vinegar sauce and figs into the pan and bring to a simmer. Let the sauce reduce by half, stirring occasionally to get any stuck on bits from the bottom of the pan. Flip the chicken in the sauce, letting the skin side sit in it for just a moment to moisten and get flavor, then serve skin side up with a healthy spoonful or two of the sauce over the top.
Get more flavor from the figs by caramelizing them in the oil before adding the sauce. Find out more in the "How to Cook" section above.
If you want to use dried figs, slice them thinly before cooking so they rehydrate enough. Also, soak them in the vinegar sauce while the chicken cooks.