In a large bowl, add ingredients for the marinade and whisk to combine. Add chicken breasts to the bowl. Refrigerate for at least 2 to 3 hours, or up to overnight.
Heat a grill or grill pan. Once the pan is hot, remove chicken from marinade and add to the grill or pan. Cook chicken until no longer pink in the center, approximately 3 to 4 minutes on either side. Then remove the grilled chicken from heat and rest for 5 minutes. Slice into thin strips and set aside until assembly.
In a medium bowl, stir together jalapeño, tomato, cilantro and red onion.
To assemble the bowls, start with brown rice as a base, dividing between the two bowls evenly. Top each bowl with pico de gallo, sliced chicken, and avocado. Finally, finish with a dollop of sour cream, lime wedges and an extra sprinkle of chopped cilantro.