Preheat the oven to 400°F with a rack in the center position.Bring a pot of water to a boil over high heat and salt it

Add the potatoes and cook for 5 minutes, or until just fork tender, then drain

Once cool enough to handle, cut the potatoes in half.Meanwhile, heat the olive oil in a large ovenproof skillet or braiser over medium-high heat

Season the chicken all over with the salt.Working in batches, add the chicken, skin side down, to the braiser and cook until the skin is browned, about 4-5 minutes

Flip the chicken and cook until browned, about 3 minutes more

Transfer the chicken to a plate

Add as many potatoes as will fit to the skillet, cut sides down, and cook until lightly browned, 1-2 minutes

Transfer the potatoes to the plate with the chicken

Repeat until all the potatoes are browned.Add the shallots to the skillet and cook, stirring, until lightly browned, 2 to 3 minutes

Stir in the garlic and cook until fragrant, about 1 minute more

Add the chicken stock and bring to a simmer

Add the chicken to the broth, skin sides up

Nestle in the potatoes and top the chicken with the lemon slices

Transfer to the oven and cook until the internal temperature of the chicken reaches 165°F on an instant-read thermometer and the potatoes are tender, about 35 minutes

Transfer the chicken to a plate

Stir in the lemon juice and butter until melted, then taste and season with salt

Return the chicken to the sauce and garnish with pepper and chives

Serve family style over cooked rice or couscous.