Chop the onions, parsley, celery, and garlic into a coarse paste in a food processor or blender.
Salt and pepper chicken, add 2-3 tablespoons of the herb blend to the chicken. Set aside. You can do this step ahead of time and let it marinate.
Heat a Dutch oven or large, heavy pot over medium-high heat. Add 2-3 tablespoons of oil to pot. Then add the chicken and sauté for 5-7 minutes, turning once, until golden brown on both sides. Transfer chicken to a plate.
Pour the rest of the herb mixture into the pot, scraping up any browned bits with a wooden spoon, stirring occasionally, for 8-10 minutes. Add about ½ a cup of chicken stock if needed.
Mix the carrots, green beans, and bell peppers into the pot. Simmer for 2-3 minutes—adjust seasonings to taste. Turn off the heat.
Cut both ends off the plantain using a sharp knife. That will make it easier to peel the plantains. Slit a shallow line down the long seam of the plantain only as deep as the peel. Remove the peel by pulling it back.
Slice plantain into rounds about an inch thick.
Heat a large or cast iron skillet with ½ inch of oil on medium-high heat until hot but not smoking.
Fry the plantain slices until golden brown, then toss them with the chicken and vegetables. Hold off on this part until you are ready to serve.
Serve immediately.