Melt butter in a large saucepan over medium heat. Add chicken and brown on all sides, about 5 minutes. Add potatoes, carrot, and onion; cook and stir until vegetables begin to soften, 6 to 8 minutes.
Stir tomato paste into the saucepan and season with salt and pepper. Pour enough water to cover and continue to simmer until chicken is no longer pink in the center and vegetables are tender, about 15 minutes. Garnish with fresh parsley.