Put the sausage and oil in a large, cold nonstick skillet and cook over medium heat until the fat starts to render and the sausage starts to brown, about 6 minutes. Transfer the sausage to a small plate with a slotted spoon.
Sprinkle the chicken with 3/4 teaspoon salt and a couple turns of pepper, then toss in the flour to coat. Increase the heat under the skillet to medium-high and sear the chicken skin-side down until golden brown, about 8 minutes.
Flip the chicken skin-side up. Add the scallion whites, garlic, jalapeno, allspice, thyme and 3/4 cup water. Return the sausage to the pan. Arrange the celery around the chicken and bring to a simmer. Reduce the heat to medium-low, cover and cook until the chicken is cooked through and the celery is crisp-tender, 20 to 25 minutes. Serve topped with the scallion greens and a few sprigs of fresh thyme.
This recipe has been updated to more accurately recognize its origin or to add cultural context. It may differ from what was originally published or broadcast.
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