Preheat a large skillet or Dutch oven over medium heat for 3-5 minutes. While it is heating, dice the onion, mince the garlic, and trim any fat from the chicken.
Once the pan is preheated, add the olive oil to the pan and swirl the pan to coat the bottom. Brown the chicken breasts on both sides, with the onion and garlic surrounding the chicken. Remove the chicken from the pan and set to the side.
Add the rice and pepper to the pan and cook until half of it turns white. Pour in 5 cups of water and the tomato paste. Stir it really well to dissolve the tomato paste, and place the the chicken back in the pot.
Cover the pot and let simmer until all the liquid has been absorbed, this can take 20-30 minutes. Taste the rice for salt. I often find that the rice has enough salt from the tomato paste, but I am salt sensitive.
Remove chicken from the pan and let rest for 5 minutes, then slice and serve over the red rice.