Combine the lemon juice, olive oil, Dijon, garlic, rosemary, salt, and pepper in a small bowl. Whisk it well to combine.
Place the chicken in a zippered plastic storage bag. Pour the marinade over the top. Press out as much air as you can and seal the bag. Use your hands to move the chicken around in the bag until it is well coated with marinade. Refrigerate for at least an hour or for up to 8 hours.
Grill the chicken on your outdoor or stovetop grill for approximately 4 to 5 minutes per side, until the internal temperature reads 165 degrees F when checked with an instant read thermometer. If using thicker pieces of chicken, cooking time will increase. If preferred, the chicken can be cooked in a little olive oil heated in a skillet on the stove.
Transfer grilled chicken to a cutting board and slice into small strips (approximately 3-inches or so). Set aside while you prepare the remaining ingredients.