Trim excess fat from chicken thighs. Cut each thigh into 2-inch pieces.
Place flour, salt, and pepper in a sealable bowl and mix well. Add half of the chicken pieces, cover the bowl, and shake to coat the pieces with the flour mixture. (As they cook, you can coat the remaining chicken pieces.)
Meanwhile, heat 2 tablespoons of olive oil over medium high heat in a large, deep skillet or Dutch oven.
When oil is shimmering, shake extra flour from chicken and place chicken pieces in a single layer in Dutch oven, being careful not to crowd them too much. Cook for about 3 minutes on one side, then flip and cook another 2-3 minutes, until a golden brown Transfer to a plate. Add remaining tablespoon of oil to pot. Once it has heated up, add remaining flour-coated chicken pieces and cook in same way as first batch. Transfer all chicken pieces to plate.
Reduce heat to medium and add garlic, capers, and lemon zest to pan. Stir constantly for 30 seconds, until they are fragrant, then add white wine. Simmer the mixture, scraping up any browned bits from the bottom of the pan. Cook about 2 minutes, until the wine mixture is reduced by half.
Add the potatoes, chicken pieces, and broth to the pot. Raise the heat and bring to a boil. Then lower the heat to simmer, cover the pot, and cook for 10 minutes.
Add the artichokes to the pot and stir to incorporate into the stewing mixture. Cover again and cook for 10-15 minutes, stirring gently from time to time, until the potatoes are tender when pierced with a fork.
Stir in the olives, parsley, and lemon juice. Season with additional salt and pepper to taste. Serve hot, with lemon wedges on the side, if desired.