Cut each chicken breast across, but not all the way through, the meat and open the breast up; pound gently and flatten to form large, very thin cutlets. Season the chicken with salt and pepper. Combine the garlic, zest, juice, tarragon and EVOO in a shallow dish and turn the chicken to coat it evenly in the mixture. Let marinate 15 minutes.
Heat a griddle or grill pan over medium-high heat. (Alternatively, the chicken can be cooked off one at a time in a large skillet.) Shake the excess marinade off the chicken and cook for 2-3 minutes on each side until cooked through and lightly browned. Discard the marinade.
Meanwhile, heat a small skillet or pot over medium heat. Melt the butter and add the shallot; cook gently for 3 minutes. Sprinkle with the curry powder and stir; whisk in the flour and cook for 1 minute more. Whisk in the broth and bring to a bubble. Add the peas and simmer in the sauce for 2 minutes.