Season the chicken thighs on both sides with kosher salt and black pepper.
Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken thighs skin side down and cook until the skin is golden brown and crispy, about 5-6 minutes. Flip and cook the other side for 3 minutes. Remove chicken and set aside.
Reduce heat to medium and add the minced garlic to the same pot. Sauté for 1 minute until fragrant, stirring frequently to avoid burning.
Pour in the chicken broth, lemon juice, and add lemon zest, dried oregano, and dried thyme. Stir to combine and bring to a simmer.
Add the halved baby potatoes to the pot. Cover and cook for 10 minutes, stirring occasionally.
Return the chicken thighs to the pot, placing them on top of the potatoes. Cover and cook for an additional 12 minutes, until the chicken is cooked through and the potatoes are tender.
Add the trimmed green beans to the pot, stir gently to combine. Cover and cook for 5 more minutes until the green beans are tender but still crisp.
Remove the pot from heat. Stir in the unsalted butter and chopped fresh parsley until the butter is melted and sauce is glossy.
Serve the chicken thighs with the lemon garlic potatoes and green beans spooned over or alongside.