Season the chicken thighs with salt and pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Sear the chicken, skin side down, until the skin is crispy and golden. This will take about 6-8 minutes per side. Remove the chicken and set aside.
In the same skillet, add the cubed sweet potatoes. Cook for about 5-7 minutes, stirring occasionally, until they start to soften and get a bit of color.
Lower the heat to medium. Add the butter and minced garlic. Sauté for about 1 minute until fragrant, then stir in the thyme and lemon zest.
Pour in the lemon juice and chicken broth. Scrape up any browned bits from the bottom of the pan; they’re flavor gold.
Nestle the chicken back into the skillet, skin side up. Cover and simmer for 15-18 minutes, or until the chicken reaches 165°F (74°C) and the sweet potatoes are tender.
If you want a glossy finish, uncover and simmer for a few more minutes to reduce the sauce slightly. Taste and adjust salt if needed.
Serve the skillet hot, spooning a bit of the lemon butter sauce over the chicken and potatoes.