Season chicken breast halves with salt and pepper.
Heat oil and butter in a large skillet over medium-high heat and sautée garlic. Fry chicken breasts in the hot skillet in batches until chicken is no longer pink in the center and juices run clear, about 5 minutes per side. Remove chicken from the skillet and keep warm.
Combine flour and melted butter in a separate tiny bowl and,set aside.
Stir white wine into the skillet, scraping any browned bits off the bottom. Whisk flour/butter mixture, chicken broth, lemon juice, Parmesan cheese, and parsley in wine; simmer until liquid is reduced by half, about 10 minutes. Add heavy cream and whisk until sauce is smooth. Stir artichoke hearts into cream sauce; continue to cook until heated through, about 5 minutes. Serve sauce over chicken.