Preheat a grill to medium high. Mix the butter, honey, 1/2 teaspoon salt and a few grinds of pepper in a small bowl.
Tear off 4 large sheets of heavy-duty foil. Divide the corn evenly among the sheets, placing it off to one side. Top with the mushrooms, scallions and thyme. Season the chicken with salt and the paprika and place on top of the vegetables. Place a heaping tablespoon of the honey butter on top. Fold the other half of the foil over the chicken and vegetables and fold the ends twice to seal, leaving room for heat to circulate.
Grill the foil packets for 8 minutes. Flip the packets, gently press and cook 6 more minutes. Flip back onto a platter to rest, 3 minutes. Carefully open the packets and top with the remaining honey butter.