Heat oil in large nonstick skillet over medium-high heat. Add chicken; sauté, turning over once, until browned and no longer pink in center, 8 to 10 minutes. Transfer chicken to large shallow bowl or pie plate. Pour Caesar dressing over the chicken; toss to coat; set aside.
Tear Romaine lettuce into bite-size pieces. Divide among 4 serving plates.
Cut each chicken breast diagonally into 1/2-inch-thick strips, keeping strips of each breast piece together. Arrange chicken on top of lettuce. Sprinkle with croutons. Spoon remaining dressing over.