Heat the oil in a large skillet over medium heat. Season the chicken with 1 teaspoon salt; add to the pan, and cook, turning once or twice, until golden brown, about 15 minutes. Pour off the excess fat.
Add the squash, tomatoes, onion, garlic, and chiles, if using. Season with additional salt, the oregano, and pepper. Cover and simmer until the chicken is cooked through and the squash is fork-tender, about 15 minutes. Transfer to a serving platter, and enjoy.
*Cook's Note: Zucchini or summer squash can be substituted. If using zucchini or summer squash, which cook faster than tatuma, add to the pan 5 minutes before the chicken is done.
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