Sprinkle chicken breasts with salt and pepper on both sides.
Place flour in shallow dish and lightly dredge each breast with flour, shaking off excess. Return floured chicken to a plate.
Heat 2 Tbsp butter in a large non-stick skillet over medium heat. Add chicken and cook until lightly browned on both sides about 4-6 minutes per side. (Chicken will not be fully cooked through). Return chicken to a clean plate.
Add 1 Tbsp butter to the skillet as well as the shallots and cook until shallots start to soften, about 3 minutes. Add the garlic and stir until fragrant, about 30 seconds Stir until cream and return chicken to the skillet. Reduce heat to medium low, cover, and cook until chicken is cooked through (160 degrees), about 5-8 minutes, turning once halfway through.
Remove chicken to serving platter. Stir the dijon mustard and tarragon into the cream sauce and season sauce with salt and pepper to taste. Simmer for about a minute to blend flavors. Spoon sauce over chicken breasts and serve.