Chop the onion, mince the garlic, and cut the chicken breast into 1-inch chunks. In a small bowl, combine the chili powder, salt, cumin, smoked paprika, oregano, and black pepper—I like to mix my spices together first so they distribute evenly throughout the chicken rather than clumping up in the pan. Slice the yellow squash and zucchini into 1/2-inch half-moons, dice the tomatoes, and chop the cilantro. Having everything prepped and ready makes the cooking process smooth and prevents overcooking any component.
Heat the corn oil in a large skillet over medium-high heat until shimmering. Add the chopped onion and cook for about 2 minutes, stirring occasionally, then add the minced garlic and cook for another minute until fragrant. Add the chicken chunks and the spice mixture from Step 1, stirring well to coat the chicken evenly with the spices. Cook for 6-8 minutes, stirring occasionally, until the chicken is cooked through and no longer pink in the center.
Add the yellow squash, zucchini, corn, and diced tomatoes from Step 1 to the skillet with the cooked chicken. Stir everything together to combine the vegetables with the spiced chicken, then reduce the heat to medium and cook for 8-10 minutes, stirring occasionally, until the squash and zucchini are tender but still have a slight bite. I find that cutting the vegetables into uniform half-moons ensures they all cook at the same rate.
Sprinkle the freshly shredded cheddar cheese evenly over the top of the chicken and vegetable mixture. Cover the skillet with a lid or foil and remove from heat, letting it sit for 3-5 minutes until the cheese melts completely. The residual heat will melt the cheese perfectly without any risk of it burning.
Transfer the chicken and squash mixture to a serving platter or individual bowls. Garnish generously with the chopped fresh cilantro from Step 1 and serve with fresh lime wedges on the side for squeezing over the top, which brightens all the warm spices beautifully.