Preheat the oven to 425°. Peel back the corn husks, leaving them attached. Discard the silk. Season the corn with salt and pepper. Replace the husks, wrap each ear in foil, transfer to a baking sheet and roast for 30 minutes, until just tender.
In a mini food processor, blend the mayonnaise with the chipotle. Add the chives; pulse. Add the oil; process until smooth.
Light a grill. Peel back the husks, leaving them attached. Brush the corn with half of the mayonnaise. Using the husks as a handle, grill the corn until lightly charred. Brush it with the remaining mayonnaise and roll in the cheese; serve with the lime wedges.