Heat a deep nonstick skillet over medium high heat.
Add a tablespoon of extra-virgin olive oil and the chicken to the pan. Season chicken with salt and pepper. Brown chicken until lightly golden all over, about 5 to 6 minutes. Remove chicken from pan and return the skillet to the heat.
Reduce heat to medium. Add another tablespoon extra-virgin olive oil and 1 tablespoon butter, the garlic and shallots to the skillet. Saute garlic and shallots 3 minutes.
Add flour and cook 2 minutes. Whisk in wine and reduce liquid 1 minute. Whisk lemon juice and broth into sauce. Stir in capers and parsley. When the liquid comes to a bubble, add remaining 1/2 tablespoon butter to the sauce to give it a little shine.
Add chicken back to the pan and heat through, 1 to 2 minutes.
Toss hot pasta with chicken and sauce and serve.
Adjust salt and pepper, to your taste. Top with fresh snipped chives.