Preheat a panini press to medium-high heat and lightly oil the surface.
Layer shredded chicken, 1 slice Cheddar cheese, 4 half-slices of bacon, and barbeque sauce on the bottom of each Kaiser roll. Top with the other half of each roll.
Grill sandwiches in the prepared panini press until cheese is melted and rolls are golden-brown, about 5 minutes.
