1. Preheat oven to 375 degrees. In a large heavy pot with a tight-fitting lid, heat 1 tablespoon oil over high. Season chicken with salt and pepper. In batches, cook chicken, skin side down, until deep golden and fat is rendered, 6 to 8 minutes. Flip and cook 1 minute more. Transfer chicken to a plate. Discard fat and wipe pot clean.

2. Reduce heat to medium-high and add remaining tablespoon oil to pot. Add onion and squash and cook until onion is translucent, 8 minutes. Add garlic and oregano and cook until fragrant, 30 seconds. Add rice and cook, stirring, until opaque, 2 minutes. Add wine and cook, stirring, until completely evaporated, 2 minutes. Return chicken to pot, skin side up, and add broth, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Bring to a boil; cover, transfer to oven, and cook until liquid is absorbed and rice is tender, 25 minutes. Let sit, covered, 10 minutes.