Melt 2 Tbsp. butter in a large skillet over medium high heat. Add onion and cook until softened, stirring occasionally, 4 to 5 minutes. Add garlic and cook 1 minute longer. Scrape into slow cooker.
Sprinkle chicken with salt. Melt remaining 2 Tbsp. butter in skillet over medium high heat until foaming. Add chicken breast halves and cook until browned, about 2 minutes per side. Transfer to slow cooker.
Add 1 cup broth and lemon juice to skillet and bring to a boil, scraping browned bits from bottom of pan. Add to the slow cooker, along with remaining broth, rice and 1 tsp. salt. Stir, cover and cook on low until chicken is cooked through and rice is tender, 2 to 3 hours. Remove chicken, stir parsley into rice and season with salt and pepper. Divide rice onto 4 plates and top each with a piece of chicken; serve immediately.