Add the white wine, olive oil, lemon juice, minced garlic, parsley, salt, and pepper to a large re-sealable plastic bag or your favourite marinating container (a glass baking dish or a glass bowl works too!). Whisk or shake the marinade ingredients together until they're combined and add the chicken breasts.
Depending on how you'll serve them, you can marinate the chicken breasts whole or you can slice them in half so they're thinner and will grill faster.
Seal the bag well or cover the container or dish and marinate for at least one hour in the fridge or they can be marinated overnight.
After the chicken pieces have marinated, preheat your grill to medium high heat.
Remove the chicken from the marinade and turn the grill to medium heat. Grill the chicken pieces over medium heat for about 8-9 minutes per side (this will depend on their size) until they're cooked through completely to an internal temperature of 165 degrees Fahrenheit (74 degrees Celsius).
Be sure to flip the chicken only once while grilling. Once you place the chicken on the grill, leave it for at least 5 minutes before checking the underside of the chicken to see if it's browned enough to flip. Once you flip the chicken, wait a few minutes and test the internal temperature of the chicken to check for doneness.
The cooking time will vary depending on the size of the chicken pieces you're using (grill thin pieces for about 5-8 minutes per side).