Combine vinegars, onion, carrot, jalapeno, garlic, black pepper, cayenne, salt, and bay leaf in a large, resealable plastic bag. Add chicken and seal bag, shaking to combine. Refrigerate, tossing chicken periodically, for at least four hours or overnight.
Heat oil in a 6-quart dutch oven or other heavy pot with a tight-fitting lid over medium-high heat. Remove chicken from marinade and pat dry; reserve marinade. Working in batches if necessary to avoid overcrowding the pot, brown chicken aggressively, skin-side down, for about 5 minutes; turn and repeat on the other side so the chicken is uniformly golden brown. Transfer to a plate.
Pour marinade through a fine strainer, reserving liquid. Add solids to the pot, adjusting heat down if necessary to avoid scorching, and cook, stirring ocassionally, until they're beginning to soften, about 5-8 minutes. Add reserved chicken and marinading liquid and cook, covered and stirring periodically, until chicken is cooked through and tender, about 30 minutes. Transfer chicken to a serving platter.
Continue to cook the onion mixture, stirring ocassionally, until liquid is mostly evaporated and the onions are soft and lightly caramelized, about 20 more minutes. Taste for seasoning, pour onions over chicken, and serve with white rice.
For a full taste of Senegal, consider serving alongside a pitcher of bisaap (iced hibiscus tea; recipe here).
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