In a large bowl, whisk shallots, lemon juice, lemon zest, Dijon mustard, olive oil, oregano, salt and pepper. Pour into a glass 13x9-inch baking dish.
Place chicken between two sheets of wax paper and pound to even thickness, about 1/2-inch thick. Add to marinade, scattering dill sprigs on top. Refrigerate 2-8 hours, turning once.
Preheat grill to medium-high. Brush and oil the grill grate. Discard marinade and dill, grilling chicken breasts 5-6 minutes per side or until cooked through.
Squeeze some lemon juice over the cooked chicken and serve with a wedge of lemon.