Heat olive oil in a large skillet over medium-high heat; cook and stir onion and garlic in hot oil for 1 minute. Add chicken; cook and stir until chicken is no longer pink, 5 to 10 minutes. Stir chicken broth, artichoke hearts with juice, sun-dried tomatoes, olives, salt, oregano, basil, and black pepper into chicken mixture; cover skillet and simmer until chicken is cooked through, about 10 more minutes.
Bring a large pot of lightly salted water to a boil. Cook angel hair in the boiling water, stirring occasionally until cooked through but firm to the bite, 4 to 5 minutes. Drain and transfer pasta to a platter; spoon chicken mixture over pasta. Sprinkle with feta cheese.
