Cook the chicken: Season chicken breasts with salt and pepper. Heat olive oil in a skillet over medium heat. Cook chicken until cooked through and no longer pink in the center. Remove from skillet and set aside.
Prepare the creamy sauce: In the same skillet, melt butter over medium heat. Sauté onion and garlic until fragrant. Add chicken broth and scrape the bottom of the skillet. Stir in heavy cream, thyme, rosemary, and parsley. Simmer for 5 minutes. Season with salt and pepper.
