Gather all your ingredients and preheat the oven to 425°F (220°C). Lightly oil a large roasting pan to prevent sticking.
In a large mixing bowl, combine chicken thighs and quartered potatoes. Pour in lemon juice, olive oil, minced garlic, dried oregano, kosher salt, rosemary, black pepper, and a pinch of cayenne. Toss everything until evenly coated with the marinade.
Arrange the chicken thighs skin-side up in the prepared roasting pan, nestling the potato pieces around them. Drizzle 2/3 cup of chicken broth over the pan and spoon any remaining marinade on top of the chicken and potatoes.
Bake for 20 minutes. Afterward, toss the chicken and potatoes gently and reposition the chicken skin-side up to ensure crispiness.
Continue baking for another 25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the skin is golden brown. Remove the chicken and transfer it to a serving platter, keeping it warm.
Turn the oven to broil. Toss the potatoes in the pan juices and broil for approximately 3 minutes, or until they are crispy and golden.
Transfer the potatoes to the platter with the chicken. Place the roasting pan on the stovetop over medium heat, adding the remaining 1/3 cup of chicken broth. Scrape up the browned bits to make a flavorful pan sauce.
Strain the pan sauce into a measuring cup and pour it over the chicken and potatoes. Sprinkle with fresh oregano before serving.