Add the spices, veggies, lime juice, and soy sauce to the chicken. Cover and let marinade for up to 4 hours, making sure to remove from the fridge 30 minutes prior to cooking.
Add oil to a skillet with high sides (and a touch of sugar if using). Reserve the bowl the chicken was marinating in. Brown the chicken (in batches if necessary), and then add all of the chicken back to the pot once done.
Add the tomato paste to the bowl the chicken was marinating in, stirring to break it up. Scrap the contents right on to the chicken and stir to incorporate.
Add water to the marinade bowl, stirring to get any leftover marinade into the water. Pour over the chicken until the chicken is mostly covered. Bring to a boil, then lower the heat and simmer, uncovered, for about an hour. Stir occasionally and adjust heat as needed. Make sure the marinade doesn't totally evaporate by adding water if needed, or if it's too thin you can turn the heat up slightly to thicken it.
Once an hour is up, dump the sliced peppers and onions into the stew, stirring to combine. Remove from the heat and cover, allowing this to steam for 5 minutes before serving.