Dice the chicken breast into bite-sized pieces and season with half of the salt, pepper, and dried thyme.
Heat the olive oil in a medium saucepan over medium heat. Add the chicken and cook until browned on all sides, then remove and set aside.
In the same pan, add the diced onion, carrots, and celery. Sauté for 3-4 minutes until the vegetables begin to soften.
Add the minced garlic and dry brown rice to the pan, stirring for 1 minute to lightly toast the rice.
Pour in the chicken broth and add the remaining salt, pepper, and thyme. Bring the mixture to a boil.
Reduce the heat to low, cover the pan with a tight-fitting lid, and simmer for 35-40 minutes or until the liquid is absorbed and the rice is tender.
Stir the cooked chicken back into the rice pilaf and let it sit covered for 5 minutes to heat through.
Garnish with fresh chopped parsley before serving.