Preheat the oven to 450°F (232°C).
Pat the chicken thighs dry and season both sides with coarse salt.
Heat 1 tablespoon olive oil in a large ovenproof skillet over medium heat until shimmering.
Add the chicken to the skillet skin-side down and cook until the skin is browned, about 5 minutes; flip the pieces.
Arrange the potatoes, smashed garlic, lemon wedges, cherry tomatoes, and thyme around and between the chicken pieces.
Pour in 1 1/4 cups chicken broth and add 1/2 teaspoon salt; bring the liquid to a gentle boil on the stovetop.
Transfer the skillet to the preheated oven and roast for about 30 minutes, stirring the potatoes once halfway through, until the potatoes are tender and the chicken is cooked through.
Remove from the oven and serve immediately, spooning some pan juices over the chicken and potatoes.