Bring a large pot of salted water to a boil. Add pasta, and cook according to package directions for al dente, about 8 minutes. (For firmer texture, reduce cooking time to 7 minutes.) Reserve 1 cup pasta cooking liquid. Drain pasta; set aside.
Sprinkle chicken with salt and black pepper. Heat oil in a large skillet over medium-high until it just begins to smoke.
Add chicken, and cook, undisturbed, until browned on 1 side, about 4 minutes. Stir and cook until evenly browned, about 3 minutes.
Add garlic and crushed red pepper to skillet, and cook until fragrant and starting to brown, about 1 minute.
Add wine and capers. Bring to a boil, and reduce by half, about 1 minute.
Add reserved pasta, ¼ cup reserved pasta cooking liquid, butter, and lemon juice. Cook over medium, stirring occasionally, until sauce clings to pasta, about 3 minutes. (Add additional cooking liquid as needed.)
Remove from heat, and stir in Parmesan and parsley. Serve with lemon wedges.