Trim the ends of the Brussels sprouts and slice them in half; dice the chicken breast into bite-sized pieces.
Place the walnuts in a dry skillet over medium heat, tossing frequently for 2-3 minutes until fragrant and toasted, then set aside.
In the same skillet, heat the olive oil over medium-high heat and add the chicken pieces, seasoning with sea salt, black pepper, and garlic powder.
Cook the chicken for 5-6 minutes until golden brown and cooked through, then remove from the pan and set aside.
Add the Brussels sprouts to the skillet cut-side down and cook undisturbed for 4 minutes until the bottoms are deeply caramelized.
Toss the sprouts and cook for another 3 minutes, then return the chicken to the pan.
Drizzle the balsamic vinegar over the mixture, tossing constantly for 1 minute until the vinegar reduces into a thick glaze.
Transfer to a plate and top with the toasted walnuts before serving.