Preheat the grill to medium-high heat.
In a mixing bowl, prepare the lime-basil butter by combining the softened butter, lime zest, lime juice, chopped basil, minced garlic, and a pinch of salt. Mix well until all ingredients are thoroughly combined and set aside.
Season the chicken thighs on both sides with olive oil, salt, and pepper.
Place the chicken thighs skin-side down on the grill and cook for approximately 6-7 minutes. Then flip and continue grilling for another 6-7 minutes on the other side, or until the internal temperature reaches 165°F (75°C).
While the chicken is grilling, add the husked corn directly onto the grill. Grill for about 10 minutes, turning occasionally, until the corn is slightly charred and tender.
Once the chicken and corn are cooked, remove them from the grill. Brush the lime-basil butter generously over the chicken and corn while they're still warm for maximum flavor.
Serve the grilled chicken thighs with the charred corn on the side, drizzled with any remaining lime-basil butter.