Mix the artichokes, Parmesan, and 1 tablespoon of the thyme in a small bowl.
Cut a 2-inch pocket in the thickest part of each chicken breast. Stuff a quarter of the artichoke mixture into each pocket.
Rub the chicken breasts with 1 teaspoon of the oil and season with ¾ teaspoon salt and ¼ teaspoon pepper.
Heat grill or grill pan to medium. Grill the chicken, turning once, until cooked through, 6 to 7 minutes per side.
Mix the tomatoes, shallot, vinegar, ¼ teaspoon each salt and pepper, and the remaining oil and thyme in a large bowl.
Slice the chicken, if desired, and serve with the tomato salad and baguette slices, if using.