In a large skillet, heat the butter and olive oil over medium heat until melted and shimmering.
Add the diced onion and sauté for 2-3 minutes, or until softened and translucent.
Stir in the minced garlic and cook for 1 minute, just until fragrant.
Add the chicken pieces to the skillet and cook, stirring occasionally, until lightly browned and cooked through, about 5-7 minutes.
Sprinkle in the flour and stir well to coat the chicken and absorb the pan juices. Let it cook briefly, about 1 minute.
Slowly pour in the chicken broth, heavy cream, and white wine while stirring constantly to prevent lumps. Add the chopped artichokes, sun-dried tomatoes, oregano, basil, salt, and pepper.
Reduce the heat to low, cover the skillet, and let the mixture simmer gently for 10 minutes, stirring occasionally.
Toss the sauce with the cooked angel hair pasta until evenly coated. Serve immediately and enjoy!