Heat grill over medium-high heat (350-400℉) and oil the grill grates (to do this, dip a wadded paper towel in a little oil and, using tongs, wipe the oil evenly over the grate. Be careful not to use too much oil, because that's a sure fire way to start a good flare-up—a little goes a long way here.)
Cook the chicken and the corn over the heat for 4-5 minutes per side, until grill marks appear and the chicken is cooked through and the corn has a nice char. The lid should be closed throughout the cooking process.
Transfer the chicken to a cutting board and let rest for 5-8 minutes before slicing and serving.
Let chicken rest for at least 5 minutes then cut into cubes. Once cool enough to handle, cut the corn off the cob.