Using a sharp paring knife, score the fat in the duck breasts a couple times in two directions to create a crosshatch pattern. Cut through the fat but not into the meat of the breast. Salt the breasts and let sit outside the refrigerator for 10 to 15 minutes to allow them to come to room temperature.
Add about 1 tablespoon olive oil to a large saute pan. Place the duck in the pan skin-side down. Bring the pan to a medium heat and cook the duck breasts low and slow to allow the fat to render and so the skin can get nice and crispy. As the fat renders out of the duck, pour or spoon it out of the pan and SAVE IT for another purpose. (It's yummy!) Cook the duck for 8 to 9 minutes on the skin side. Turn the duck over and cook the duck for 2 to 3 minutes on the flesh side. Remove the duck from the pan, cover with foil and let rest for about 10 minutes.
Add the grapes to the pan with the bacon and bring the pan to a medium heat. Cook the grapes until they split and let out their juices and the bacon is crisp.
Spoon half the grapes out of the pan and reserve. Add the port and vinegar to the pan, season with salt and reduce the port by half. Add the chicken stock and reduce it by half. Add in the reserved grapes. Taste and re-season if needed.
Slice the duck on a severe bias and serve garnished with the sauce.