Coat a large nonstick skillet with cooking spray; place over medium heat until hot. Add chicken; cook 7 minutes on each side or until done. Remove chicken from skillet; let cool slightly, and coarsely chop chicken.
While chicken cooks, combine vinegar and next 5 ingredients in a small bowl, stirring well with a wire whisk.
Combine chicken, cucumber, green onions, and salad greens in a large bowl. Add vinegar mixture, and toss well. Serve immediately.