Combine the olives, lemon zest and garlic in a small bowl. Set aside.
Mix the smoked paprika, olive oil, 3/4 teaspoon of the salt and pepper into a paste in a large bowl.
Lay the chicken thighs skin-side down. Using a pair of kitchen shears, make a cut down the length of the bone to expose it, then cut the meat away from the bone. Discard the bone. Add the boned chicken thighs to the paste and massage to coat.
Thinly slice the potatoes on a mandoline, about 1/4-inch thick. Arrange the potato slices and onion pieces in an even layer on a foil-lined half sheet pan and sprinkle with the remaining 3/4 teaspoon salt.
Stuff about 2 tablespoons of the olive mixture under the skin of each chicken thigh. Arrange the chicken thighs, skin-side up, on a cooling rack and set the rack over the potatoes and onion in the half sheet pan. Bake until the skin is crispy and the potatoes are tender, 55 to 60 minutes. If you prefer the potatoes crispy, remove the rack with the chicken and return to the oven for an additional 5 to 10 minutes. Serve immediately.