The Navy Precision Optical Interferometer (NPOI) has a station layout which makes it uniquely suited for imaging. Stellar surface imaging requires a variety of baseline lengths and in particular long baselines with resolution much smaller than the diameter of the target star. Because the fringe signal-to-noise ratio (SNR) is generally low on such long baselines, fringe-tracking cannot be carried out on those baselines directly. Instead, baseline bootstrapping must be employed in which the long baseline is composed of a number of connected shorter baselines. When fringes are tracked on all the shorter baselines fringes are also present on the long baseline. For compact sources, such as stellar disks, the shorter baselines generally have higher SNR and making them short enough that the source is unresolved by them is ideal. Thus, the resolution, or number of pixels across a stellar disk, is roughly equal to the ratio of the length of the long baseline to the length of the short baselines. The more bootstrapped baselines, the better the images produced. If there is also a wide wavelength coverage, wavelength bootstrapping can also be used under some circumstances to increase the resolution further. The NPOI is unique in that it allows 6-station, 5-baseline bootstrapping, the most of any currently operating interferometer. Furthermore, the NPOI Classic beam combiner has wavelength coverage from 450 nm to 850 nm. However, until now, this capability has not been fully exploited. The stellar surface imaging project which was recently funded by the National Science Foundation is exploiting this capability. The New Classic data acquisition system, reported separately, is the hardware which delivers the data to the fringe-tracking algorithm. In this paper we report on the development of the fringe-tracking capability with the New Classic data acquisition system. We discuss the design of the fringe tracking algorithm and present performance results from simulations and on sky observation.