Preheat your oven to 375°F (190°C).
Season the chicken breasts with salt and pepper.
Heat olive oil in a large oven-safe skillet over medium-high heat. Add the chicken breasts and sear until golden brown, about 3-4 minutes per side.
In a small saucepan, combine pomegranate juice, honey, balsamic vinegar, thyme, and red pepper flakes. Bring to a simmer over medium heat, and reduce by half until thick and syrupy, approximately 10-15 minutes.
Brush the chicken with the pomegranate glaze, reserving some for serving.
Transfer the skillet to the oven and bake the chicken for 20 minutes, or until the internal temperature reaches 165°F (74°C).
While the chicken is baking, melt butter in a small pan over medium heat. Add the chopped walnuts and a pinch of salt. Toast them until they are golden and fragrant, about 5 minutes, stirring frequently.
Once the chicken is done, let it rest for a few minutes, then sprinkle with the toasted walnut crunch.
Drizzle the remaining pomegranate glaze over the chicken before serving.