Remove chicken from fridge before you start to prep the other ingredients so it can come to room temperature. Season legs generously with sea salt and pepper. Heat oil in a medium Dutch oven or heavy shallow pot over medium-high. Place chicken in the pot, skin side down, and cook until skin is deep golden brown, 10–12 minutes. Transfer to a plate.
Reduce heat to medium and add leeks to same pot. Cook, stirring occasionally, until they’re very soft and just beginning to brown, 8–10 minutes. Add tomatoes and cook, stirring occasionally, until tomatoes are softened and release their juices, 6–8 minutes. Put chicken back in the pot, skin side up. Cover, reduce heat to low, and simmer gently until legs are cooked through, 45–60 minutes.
Uncover pot, add lemon wedges and continue to simmer until juice thickens and meat is close to falling off the bone, about 20 minutes. Season with sea salt and pepper, to taste; and serve with a side of white rice.