1. Season chicken with salt and pepper. Heat a large straight-sided skillet over medium-high. Add oil, then chicken, skin-side down, in a single layer. Cook, turning, until browned, 12 to 15 minutes. Transfer to a plate.

2. Reduce heat to medium. Add garlic and artichokes; cook until golden brown in places, 5 to 7 minutes. Add olives, oregano, and flour; cook, stirring constantly, 30 seconds. Stir in broth and lemon, scraping browned bits from bottom of pan. Return chicken, skinside up, and any juices to pan; bring to a simmer. Partially cover, reduce heat to low, and simmer until a thermometer inserted in thickest part of chicken (without touching bone) registers 165 degrees, 10 to 12 minutes. Remove lid; continue simmering until sauce thickens slightly. Serve over orzo, sprinkled with oregano leaves.