In a large nonstick skillet, heat oil over medium-high heat; add chicken and cook until browned, about 5 minutes per side. Transfer to a plate.
Add chicken broth to skillet; bring to a boil over high heat. Add pasta; reduce heat, cover and simmer until pasta is tender, 12-14 minutes. Return chicken and accumulated juices to skillet; cook until chicken is cooked through, 2-3 minutes. Remove chicken to cutting board.
Add watercress to skillet, stir and cook until wilted, 1 minute. Return chicken and accumulated juices to skillet; heat through.
Top each serving with Parmesan and serve with lemon wedges, if desired.
