A coiled tubing injector system includes a traction system for advancing coiled tubing through the injector and into or out of a well. The traction system includes a plurality of carriers (129) and gripper shoes (128) configured to repeatedly propagate through the injector along guides (114). The traction system also includes a position monitor (134) for monitoring the lateral position of the carrier, gripper shoe, or portion thereof as the carrier and gripper shoe propagates along the coiled tubing path.