Preheat the oven. Preheat your oven to 350°F (175°C).
Season the chicken. Pat the chicken thighs dry with paper towels, then season generously with salt and black pepper.
Sear the chicken. Heat the olive oil in a large oven-safe skillet over medium heat. Place the chicken thighs skin-side down and sear for approximately 3–4 minutes per side, until nicely browned. Transfer the chicken to a plate.
Cook the shallots. Add the butter to the same skillet. Once melted, add the sliced shallots with a small pinch of salt and pepper. Cook for 3–4 minutes, stirring frequently, until softened.
Add the aromatics. Stir in the garlic, thyme, and red chili flakes. Cook for about 30 seconds, just until fragrant.
Make the balsamic sauce. Add the balsamic vinegar, chicken broth, Dijon mustard, and honey. Stir well, scraping up the flavorful browned bits from the bottom of the skillet. Bring to a gentle simmer and cook for about 1 minute.
Add chicken and figs. Return the chicken thighs to the skillet and arrange the halved figs around them. Spoon a little sauce over the chicken.
Bake. Transfer the Skillet Balsamic Chicken With California Figs to the oven and cook for approximately 15–20 minutes, or until the thickest part of the chicken reaches at least 165°F (74°C), avoiding the bone when checking.
Finish and serve. Carefully remove the skillet from the oven and squeeze fresh lemon juice over the chicken and figs. Spoon the balsamic sauce over each serving and enjoy warm.