Step 1

Preheat oven to 350 degrees F (175 degrees C).

Step 2

Heat olive oil in a skillet over medium heat; cook and stir shallot until translucent, about 5 minutes. Pour balsamic vinegar into skillet and bring to a boil. Reduce heat to low and simmer until balsamic vinegar mixture is reduced by half, about 10 minutes. Stir often.

Step 3

Cut chicken breasts from one side through the middle horizontally to within one-half inch of the other side. Open the two sides and spread them out like an open book.

Step 4

Spread half the goat cheese onto one half of each chicken breast and drizzle 1/3 of the reduced balsamic vinegar mixture over the goat cheese. Close the chicken breasts over the goat cheese and secure with toothpicks. Arrange chicken into a baking dish. Drizzle with remaining 1/3 of the balsamic reduction.

Step 5

Bake in the preheated oven until the chicken is no longer pink inside, the filling is hot, and the juices run clear, 30 to 35 minutes. An instant-read meat thermometer inserted into the center of a filled breast should read at least 160 degrees F (70 degrees C).