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In a large Dutch oven or heavy pot, heat oil over medium-high. Season chicken with salt and pepper. Working in two batches, cook chicken until browned on all sides, 6 to 8 minutes per batch. Transfer to a plate. Pour off all but 1 tablespoon fat and return pot to heat.
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Add garlic, tomatoes, and oregano; cook until fragrant, about 30 seconds. Add wine and cook, scraping up browned bits, until almost evaporated, about 1 minute. Add broth; return chicken, skin side up, to pot. Bring to a boil; reduce to a simmer, cover, and cook 15 minutes. Add zucchini; season with salt and pepper. Cover; simmer until chicken is cooked through, 10 to 15 minutes. Stir in lemon juice.
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Meanwhile, in a large saucepan, combine 4 1/2 cups water, 1 1/2 teaspoons salt, and teaspoon pepper and bring to a boil. Whisking constantly, slowly add cornmeal. Reduce heat to medium-low and cook, whisking frequently, until polenta has thickened, 20 to 25 minutes; whisk in butter. Serve chicken and vegetables over polenta.