Place one chicken breast on cutting board. Holding knife blade parallel to board and starting at thickest long side, slice horizontally to make two thin cutlets. Repeat with remaining chicken.
Sandwich chicken between plastic wrap; using meat mallet or heavy-bottomed saucepan, pound to ½ in (1 cm) thickness. Sprinkle with 1 tsp of the salt and ½ tsp of the pepper.
In large skillet, heat oil over medium-high heat; working in batches, cook chicken, flipping once, until browned, 2 to 3 minutes per side. (Chicken does not need to be cooked through.) Remove to a plate. Reduce heat to medium.
Add garlic to pan and cook until fragrant, about 1 minute. Stir in water, scraping up any browned bits.
Add canned tomatoes with juices, breaking up tomatoes with your hands as you add them. Stir in sugar, basil and oregano. Return chicken to pan, flipping to coat with sauce.
Cover and cook over medium heat until chicken is cooked through, 11 to 14 minutes. Remove chicken from sauce and let rest for 5 minutes.
While chicken is resting, stir in Roma tomatoes and cook until heated through, about 3 minutes. Sprinkle with remaining ¼ tsp each salt and pepper or to taste. Serve the sauce over the chicken and sprinkle with fresh basil. (See note #2.)