Melt the butter in medium saucepan on the grates of the grill. Whisk in the flour and cook for 1 minute. Add the hot milk and whisk until smooth and thickened, 5 minutes. Whisk in both cheeses and season with salt and pepper, to taste. Remove from heat.
Put heavy duty aluminum foil on the grill and top it with potato chips. Allow them to heat through, about 2 minutes.
Transfer potato chips to a platter, drizzle with the cheese sauce and sprinkle with chives.