Season chicken breasts on both sides with salt and pepper. Heat 1 ½ teaspoons oil in large skillet over medium high heat, and chicken and sear until well browned on both sides, about 3 minutes per side. Remove chicken to plate and keep warm.
Reduce heat to medium, add the remaining 1 ½ teaspoons of oil to plan. Add onion and garlic, stirring for 1 minutes.
Whisk broth and flour and 1 tablespoon dill and lemon juice in small bowl and add to pan, stir in white wine. Remove chicken and any accumulated juices to pan; reduce heat to low and simmer until chicken is cook through, about 4 minutes.
Remove chicken to platter, season sauce with salt and pepper and spoon over chicken, garnish with remaining dill.
*Adopted from La Crosse Tribune