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Step 1
Season chicken with salt and pepper. Heat 1 tablespoon oil in a Dutch oven over medium-high. Working in batches, sear chicken, turning occasionally to brown and crisp skin evenly, about 8 minutes per batch. Transfer chicken to a plate.
Step 2
Add remaining 3 tablespoons oil to chicken drippings in pan over medium-high. Add bell peppers and onions, turning and folding using tongs to coat in fat as they begin to wilt, scraping bottom of pan to loosen and incorporate browned bits. Continue folding until vegetables have reduced in volume by half, about 5 minutes. Add garlic and Italian seasoning, and stir to combine. Reduce heat to medium-low, and cook, stirring occasionally, until vegetables have softened and are beginning to caramelize but still hold their shape, about 25 minutes.
Step 3
Crush tomatoes by hand, and add to pan with juices from can. Fold to combine with vegetables. Bring to a simmer over medium-high. Reduce heat to medium-low, and cook, stirring occasionally, until sauce is slightly thickened, about 10 minutes. Season to taste with salt. Add chicken pieces to sauce, nestling them into a snug single layer. Cover, reduce heat to low, and cook until a thermometer inserted in thickest portion of several pieces of chicken registers 155°F, 20 to 25 minutes. Remove pan from heat, and let stew rest, covered, at least 10 minutes before serving. Garnish with basil and oregano.