Slice each chicken breast like you were going to butterfly it, cutting it in two, creating a total of four chicken breast pieces.
Season with salt and pepper.
Preheat a large sauté pan over medium high heat.
Add butter and olive oil.
Sauté chicken breasts until browned, 2-3 minutes per side.
Remove from pan, cover and reserve.
Reduce heat to medium, and in the same pan add shallot, red pepper flakes, garlic, rosemary, and lemon zest.
Cook until shallot is translucent, but not browned, 2-3 minutes.
Add grape tomatoes and salt & pepper to taste.
Sauté until tomatoes start to give off their juices, 5-7 minutes.
Add artichoke hearts and heat through, 2-3 minutes.
Stir in lemon juice and chopped parsley.
Adjust seasonings and remove from heat.
Place about ¼ of the tomato artichoke mixture on top of each chicken breast piece.
Serve on firm polenta, mashed potatoes, or your favorite starch dish.