Pound chicken breasts in thick parts, to make them an even thickness; probably about 1/2 inch thick
Use an immersion blender or regular blender to blend and emulsify the Dijon mustard and the olive oil, along with the tarragon and pepper. This is an important step - don't skip! It changes the texture of the Dijon-oil mixture so it can coat the chicken well.
Put the mustard-olive oil mixture in a gallon-size plastic ziploc bag and add the chicken breasts. Leave them anywhere from 15 minutes to - overnight (in the refrigerator). Let come to room temp. before grilling.
Preheat a gas grill to low; oil the grates. Add the chicken, leaving a fairly thick coating of the mustard mixture on both sides of the chicken (in other words don't scrape off the marinade). Depending on your grill - cook 3-4 minutes on the first side; it should un-stick by itself and show browned grill marks; another 3-4 minutes on the second side, JUST until fairly firm and done in the middle. Serve with your favorite easy salad or vegetable.