Gather all ingredients.
Whisk flour, pepper, and paprika together in a shallow dish. Dredge chicken in flour mixture until evenly coated.
Heat oil in a large skillet over medium-high heat. Add garlic; cook and stir until golden and fragrant, about 1 minute; transfer to a plate.
Melt 2 tablespoons butter in the same skillet. Add chicken and cook until browned, about 5 minutes per side; transfer to a plate.
Pour wine into the hot skillet and bring to a boil over high heat, scraping the browned bits from the bottom and sides of the pan with a wooden spoon. Boil until wine is reduced by half, about 5 minutes.
Whisk in chicken broth, reserved garlic, lemon juice, and capers; cook for 5 minutes.
Stir in parsley and remaining 2 tablespoons butter.
Reduce the heat to medium, return chicken to the skillet, and continue cooking until sauce thickens, about 15 minutes.
Bring a large pot of lightly salted water to a boil. Cook angel hair pasta in the boiling water, stirring occasionally, until tender yet firm to the bite, 4 to 5 minutes. Drain well.
Transfer chicken pieces to a serving dish and drizzle with a few tablespoons sauce. Add cooked pasta to the skillet and toss to coat with remaining sauce. Portion noodles onto serving plates and top with chicken.
