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 3/4 teaspoon salt and 1/4 teaspoon pepper.
Heat a 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, 1/4 teaspoon salt, 1/4 teaspoon 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.
Substitution: If you don't care for artichokes, try stuffing the chicken breasts with one of the following: olive tapenade; Feta and pine nuts; or roasted red peppers and Parmesan.