A fiber tracking system was constructed at UCLA, consisting of four layers of scintillating fiber ribbons coupled to visible light photon counters (VLPCs), and was tested by measuring cosmic ray tracks. The total length of the fiber array is 7 m: 4 m of scintillating fiber and 3 m of clear optical fiber, 0.83 mm diameter. An average number of 6 photoelectrons were detected by the VLPCs, 7 m from the cosmic ray interaction point at the end of the fibers. The details of the experimental arrangement and the test results are presented.