Marinate: In a small bowl whisk together the balsamic vinegar, olive oil, dijon mustard, rice vinegar, lemon zest, garlic, soy sauce and pinch of salt and pepper. Place chicken in a glass container or resealable silicone bag. Pour marinade over the chicken and ensure it is fully coated. Place in refrigerator and let marinate a minimum of 30 minutes or up to 3 hours.
Prep Grill: Bring grill to medium-high heat (about 400 degrees F) and ensure grill grates are clean.
Grill Chicken: Grill chicken on direct heat (directly over flame) for 3-4 minutes per side (the bigger/thicker the thigh the longer you will need to cook it), flipping once. Remove from grill once the internal temperature has reached 165 degrees F (use an instant-read meat thermometer). Let rest 5-10 minutes before serving.
Tomatoes: Meanwhile, place the tomatoes in a medium-sized bowl. Drizzle with olive oil and season with salt. Toss to coat. While the chicken rests place the tomatoes on the grill pan over direct heat. Move around as they start to char, approx. 5 minutes or so.
Mozzarella: Once the tomatoes are slightly charred add the mozzarella and close the grill for 1-2 minutes - just until the cheese is bit warmed (you obviously don't want the cheese to get to the point of melting - we are just looking to warm them up a bit here so keep a close eye on them). Transfer tomatoes and mozzarella pearls to a plate.
Build Bowls: Divide rice, chicken thighs, tomatoes and mozzarella between 4 bowls. Garnish with fresh basil and drizzle with balsamic glaze.
Notes
Chicken Breast: feel free to sub in boneless chicken breasts here - just adjust the cook time accordingly.
Mozzarella Pearls: I would use these right out of the refrigerator so you don't run into any issues with melting - I was a little nervous testing this recipe (I thought they would melt right away - they were just fine).