Pat the chicken thighs dry with paper towels and trim off any large pieces of fat. Season both sides with 1 teaspoon of the salt and the black pepper.

Set a large deep skillet with a lid over medium-high heat and add the olive oil. Let the oil heat until it looks loose and shiny, about 1 minute.

Put the chicken thighs into the skillet in a single layer. Cook without moving them until the first side is browned, 4 to 5 minutes.

Turn the chicken over in the skillet. Cook until the second side has some brown color but the chicken is not fully cooked through, 3 to 4 minutes.

Transfer the chicken to a plate. Leave the browned bits and fat in the skillet because they flavor the rice.

Lower the heat to medium and add the sliced onions to the skillet. Sprinkle them with 1/4 teaspoon of the salt.

Cook the onions, stirring every couple of minutes, until they soften and turn deep golden brown, 12 to 15 minutes. If they start to darken too fast, lower the heat a little.

Add the chopped garlic and thyme leaves to the onions in the skillet. Stir for about 30 seconds, just until they smell fragrant.

Add the rice to the skillet. Stir for 1 minute so the grains are coated with the onion mixture.

Pour the chicken broth into the skillet and sprinkle in the remaining 1/4 teaspoon salt. Use a wooden spoon to scrape up any browned bits stuck to the bottom of the skillet.

Raise the heat and bring the liquid to a gentle boil. Spread the rice into an even layer in the skillet.

Return the chicken and any juices from the plate to the skillet, setting the chicken on top of the rice. Keep the pieces mostly above the liquid so the rice can cook underneath them.