Spread 1 ounce goat cheese over each chicken breast. Top each with 1 tablespoon of sun dried tomatoes and sprinkle with 1 tablespoon basil. Roll up jelly roll style and secure with toothpicks.
In a large frying pan, heat butter and olive oil over medium heat. Add chicken; cook, turning, until lightly browned outside and white but still moist inside, 10-12 minutes. Remove and set aside.
Pour off all but 1 tablespoon fat from pan. Add broth and remaining 2 tablespoons sun dried tomatoes. Boil until reduced by half.
To serve, remove picks from chicken; cut crosswise on the diagonal into ½ inch slices. Arrange on plates and spoon about 1 tablespoon sauce over each serving.