In a small bowl, whisk together the lemon juice, mustard, 1 teaspoon salt and 1/2 teaspoon pepper. While whisking, slowly add the olive oil until the vinaigrette is emulsified. Set aside.
Place the chicken breasts in a baking dish large enough to hold them in a single layer and sprinkle generously with salt and pepper on both sides. Pour half the marinade over the chicken, reserving the other half to use later. Allow the chicken to marinade for at least two hours in the refrigerator.
Preheat the oven to 350 degrees F.
Roast the chicken for 35 to 40 minutes, or until cooked through. Remove the chicken from the oven and pour the remaining marinade over the top of the chicken. Cover the dish with aluminium foil and allow to rest for 10 minutes.