In a very large ovenproof skillet, heat 1/2 cup plus 2 tablespoons of the olive oil. Add the onions, bell peppers, and garlic and cook over moderately high heat, stirring occasionally, until softened and lightly browned, about 10 minutes. Add the tomatoes and cook until softened and all of the liquid has evaporated, about 10 minutes longer.

Transfer the vegetables to a blender and puree until smooth. Season the vegetable puree with salt and Piment d'Espelette.

Wash and dry the skillet. Heat 3 tablespoons of the oil in each of 2 very large ovenproof skillets. Season the chicken with salt and pepper. Add 10 of the thighs to each skillet, skin side down. Cook over moderately high heat, turning once, until the chicken is golden brown, about 12 minutes. Remove from the heat. Transfer the chicken to a platter and pour off the fat in the skillets.

Add 1/4 cup of the brown sugar to 1 of the skillets and cook over high heat, whisking constantly, until melted, about 1 minute. Off the heat, carefully whisk in 1/2 cup of the vinegar; turn away to avoid the fumes. Cook over moderate heat, whisking and scraping up any browned bits from the bottom of the skillet, until thick and syrupy, about 1 minute. Add half of the vegetable puree and bring to a boil. Return 10 of the chicken thighs to the skillet, skin side up. Repeat with the second skillet and the remaining 1/4 cup sugar, 1/2 cup of vinegar, puree and chicken thighs. Cover both skillets and simmer the chicken over low heat until cooked through, about 12 minutes.

Preheat the broiler and position a rack 8 inches from the heat. Uncover the skillets and broil the chicken until the skin is lightly browned and crisp, about 2 minutes. Transfer the chicken to a platter, spoon the sauce on top, and serve.

Piment d'Espelette is a smoky, mildly spicy ground chile native to the Basque region. It is available at specialty food shops, spice shops and by mail order from Piperade (415-391-2555 or piperade.com).