Marinate chicken breasts in balsamic vinegar, olive oil, oregano, lemon zest and salt in a large ziploc bag or shallow pan for about 20 minutes (while preparing other ingredients)
Meanwhile, cook pasta in boiling salted water, according to package directions, drain and set aside
Heat outdoor grill or grill pan over medium-high heat and rub marinade off of chicken with a paper towel before grilling for about 4 minutes on each side or until fully cooked through, temperature should be 165 degrees. (Rubbing off the marinade prevents it from burning). Allow chicken to rest for about 5 minutes and then cut into chunks.