Place the garlic, olive oil, chipotle chili powder, vinegar, lime juice, salt, pepper, paprika, and oregano in a blender and blend until smooth. Combine with the chicken in a resealable plastic bag; marinate for at least 30 minutes, overnight preferred.
Make the Pico de Gallo: Salt the diced tomato; leave in a colander to drain for 20 minutes. Combine the drained tomatoes with the remaining ingredients and set aside.
Grill the chicken over direct medium-high heat until it reaches an internal temperature of 155°F, about 10 minutes, flipping halfway through. Let the chicken rest for 5 minutes, then chop it into bite-sized chunks.
Make the Cilantro Rice: Place the cooked rice in a big bowl. Mix in the oil. Add the lime and lemon juices and salt, stirring together. Finally, stir in the cilantro. Taste and add more salt or lime juice if you like.
Serve the burrito bowls any way you see fit. At my house, we like rice, then lettuce, then chicken, then pico, then guac.