In a small microwave-safe bowl, combine the soy sauce, sesame oil, honey, ginger, and garlic. Heat in microwave on medium power for 1 minute, then stir. Heat again for 30 seconds.
Pour soy sauce mixture over chicken breasts in a shallow dish or bowl, and marinate in the fridge for 15 minutes.
Preheat an outdoor grill for medium-high heat and lightly oil grill grate.
Cook chicken on the prepared grill 5 to 8 minutes per side, or until no longer pink and juices run clear. Baste frequently with remaining marinade.