In a small bowl, mix olive oil, smoked paprika, cumin, salt, and pepper. Rub the mixture all over the chicken breasts. Brush the corn ears lightly with olive oil.
Preheat a grill or grill pan to medium-high heat. Grill the chicken for 5-7 minutes per side, until internal temperature reaches 165°F. Grill the corn, turning occasionally, for 10-12 minutes until charred in spots. Remove and let rest.
In a medium bowl, whisk together Greek yogurt, mayonnaise, lime juice, minced garlic, salt, and chipotle chili powder until smooth. Set aside.
Once cool enough to handle, cut the corn kernels off the cobs. Slice the grilled chicken into bite-sized strips or cubes.
In a large bowl, combine the grilled corn, diced cucumber, red onion, and cilantro. Add the dressing and toss gently. Fold in the chicken. Taste and adjust salt or lime.
Transfer the salad to a glass serving bowl. Garnish with crumbled cotija cheese and lime wedges. Thread some chicken pieces onto bamboo skewers for a fun presentation.