Cook chicken in a large stockpot of boiling water for 45 minutes with the lid on.
Remove chicken from liquid to cool. Reserve 1 cup of the chicken stock & freeze the rest. Please don’t throw it away – that’s good stuff! Skin, bone, & chop chicken.
Saute onion & bell pepper in hot oil in your large stockpot until tender. Add chopped chicken, tomato, & next 4 ingredients.
Combine flour & 1 cup of reserved chicken stock, whisking until smooth. Stir into chicken mixture. Add potato & next 5 ingredients.
Cover & cook over medium heat, stirring occasionally, for 40 minutes. Add corn and lima beans. Cook for 10 additional minutes. Add in the bbq sauce, starting with 1/2 cup. Taste & add more depending on your tastes.