Pound the chicken breasts so they are even in thickness, about 1/2 inch. Place in a zip-top bag.
In a small bowl, whisk the olive oil, vinegar, mustard and honey.
Pour half (1/2) of the marinade into the bag over the chicken, reserving the other half for later.
Seal the zip-top bag removing excess air and massage the marinade into the chicken. Place on a dish and refrigerate 2 hours or more.
In a bowl, combine all of the salsa ingredients, toss and reserve at room temperature.
Preheat a clean grill to high and oil the grates. Meanwhile, remove the chicken from the fridge and season with salt and pepper on both sides, throwing away the bag with leftover marinade that was in contact with the raw meat.
Place the chicken breasts on the grill and cook 4 minutes. Flip and cook another 4 minutes. Move to indirect heat, brush the chicken breasts with reserved balsamic marinade and cook another 3 minutes per side or until an instant-read thermometer reads 74 degrees C/165 degrees F.
Remove the chicken from the grill and serve with the strawberry avocado salsa.