Preheat the oven to 350°F.
Pat the chicken thighs dry with paper towels.
Add the chicken thighs and potatoes to a large bowl. Add 2 tablespoons olive oil, cumin, oregano, salt, and black pepper. Toss until the chicken and potatoes are evenly coated.
Arrange the potatoes around the outside of a cast iron skillet or sheet pan. Place the chicken thighs in the center in a single layer.
Roast for 25 minutes.
Toss the green beans with 1 teaspoon olive oil and a pinch of salt.
Remove the skillet from the oven. Stir the potatoes and add the green beans around the chicken.
Return the skillet to the oven and continue roasting for 20 to 25 minutes, or until the chicken is cooked through.
Transfer the chicken to a plate and set aside. Increase the oven temperature to 425°F. Stir the potatoes and green beans and continue roasting for about 15 minutes, or until the potatoes are fork-tender and lightly browned.
While the potatoes and green beans finish roasting, make the cilantro lime sauce. Add the cilantro, olive oil, lime juice, grated garlic, jalapeño, salt, and black pepper to a small bowl. Stir until combined.
Remove the skillet from the oven and return the chicken to the skillet. Let everything rest for about 5 minutes.
Spoon about two-thirds of the cilantro lime sauce over the chicken, potatoes, and green beans. Gently toss the potatoes and green beans to lightly coat them.
Drizzle the remaining cilantro lime sauce over the chicken just before serving.