In a mixing bowl, combine garlic, cumin, oregano, salt, black pepper, and lime juice. Add chicken thighs and coat well. Let marinate for at least 30 minutes.

Heat vegetable oil in a large skillet over medium heat. Add marinated chicken and cook for about 25-30 minutes, turning occasionally, until golden brown and cooked through.

In the same skillet, remove excess oil if necessary. Add sliced plantains and fry until golden brown on both sides, about 3-4 minutes per side.

Plate the fried chicken alongside the crispy plantains. Serve hot.