Preheat the oven to 350 degrees F.
Season the chicken breasts with salt and pepper. Heat the oil in a large skillet over medium-high heat. When the oil is hot, sear the chicken breasts until golden brown, 3 to 4 minutes per side. Remove the seared chicken to a baking sheet with sides and finish cooking in the oven until an instant read thermometer reads 165 degrees F, or about 10 minutes.
While the chicken is in the oven, deglaze the skillet with 1/4 cup of the reserved pear juice and balsamic vinegar. Continue to cook and stir over medium heat until the liquid is slightly reduced and syrupy. Whisk in the butter until just incorporated and season to taste with additional salt and pepper.
Add the pear halves to the pan, turning once to coat them on both sides. Remove the pan from the heat.
To serve, place a chicken breast on each of four plates. Drizzle the chicken with the pan sauce, place a pear half next to it and fill the pear’s cavity with blue cheese. Crumble additional cheese over chicken breast as garnish and serve immediately.
Preheat the oven to 350 degrees F.
Season chicken breasts with salt and pepper. Heat 3 tablespoons olive oil in large skillet over medium-high heat; sear half of the chicken breasts until golden brown on each side. Remove seared chicken to baking sheet with sides and repeat with remaining olive oil and chicken. Place the baking sheets in the oven to finish cooking.
While chicken is in the oven, deglaze skillet with 1-1/2 cups of the reserved pear juice and balsamic vinegar. Stir over medium heat until liquid is slightly reduced and syrupy; whisk in butter just until incorporated. Season to taste with additional salt and pepper as needed.
Add pear halves to the pan, turning once to coat with sauce on both sides. Remove pan from heat.
To serve, place chicken breasts on individual plates or a large platter. Drizzle with sauce. Place a pear half next to each chicken breast, and fill its cavity with blue cheese. Crumble additional cheese over chicken breast as garnish.