Combine the chili powder, salt, paprika, cumin, and cayenne pepper in a small bowl. Add the chicken thighs to a large bowl, add half of the spice mix, and toss to evenly coat.
Heat the oil in a large skillet over medium heat. Once the oil is shimmering, add the chicken thighs in one single layer (you may need to cook in two batches depending on the size of your pan). Cook until crisp on each side and each reaches an internal temperature of 165°F, about 6 to 8 minutes per side. Transfer to a large dish, leaving any remaining oil in the skillet.
To the same skillet, add the rice and cook, stirring frequently, until toasted, about 1 minute. Add the garlic, corn, and the remaining spice mix and mix well. Continue cooking, stirring occasionally, to warm the corn and brown it slightly, 2 to 3 minutes.
Stir in the coconut milk and 1 ½ cups of the broth, turn the heat to medium-high, and bring to a light boil. Reduce the heat to medium-low, cover, and cook until the rice is tender, 14 to 18 minutes, stirring halfway through to prevent sticking (Note: If needed while the rice cooks, stir in the remaining ½ cup broth).
Squeeze the lime juice over the rice and mix. Return the cooked chicken on top of the rice and sprinkle with the crumbled cotija or feta (if using) and chopped cilantro. To serve, evenly divide among 4 plates.
