Pat chicken dry with a paper towel and salt and pepper to taste. In a large skillet using one tablespoon of the oil brown the chicken breasts on both sides; remove from the skillet and set aside.
Add the other tablespoon of oil to the skillet and cook the shallots until tender, add the artichoke hearts, and cook until starting to brown, and then stir in the cream and cheese.
Add the chicken back into the skillet and cook on simmer for about 10 minutes-turn the chicken and continue cooking until the internal temperature of the chicken reaches 160F. remove chicken and set aside on a serving plate.
Mix the tomatoes and parsley into the sauce. Salt and pepper to taste; serve the sauce over the chicken.