Rinse leeks, pat them dry, and season all over with salt and pepper.
Heat a large, dry skillet, preferably cast-iron, over medium-high heat for 2 minutes.
Add leeks to pan, cut side down, and cook, shaking pan occasionally, until evenly charred on cut side, about 4 minutes (charred is a nice way of saying burned; things could get a little smoky).
Turn leeks over and add ghee and ¾ cup water to the skillet.
Reduce to a simmer and cook until leeks are tender when pierced with a cake tester and liquid is almost completely evaporated, about 4 minutes longer.
Transfer leeks to a serving plate. Crush potato chips with your hands and let the pieces rain down on the leeks, then top with chives.