On May 27, 1997, approximately 1900 mountain daylight time, a Piper PA-31-350, N491SC, operated by Sundance Air, Inc., as flight 6416, nonscheduled domestic cargo service, was substantially damaged when the left engine cowling separated inflight and struck the vertical stabilizer about 30 miles north of Greeley, Colorado. The commercial pilot was not injured. Visual meteorological conditions prevailed and an IFR flight plan had been filed. The airplane was being operated under Title 14 CFR Part 135. The flight departed at 1630 from Scottsbluff, Nebraska, and was en route to Colorado Springs, Colorado. According to the pilot, he was in cruise flight when he observed the left front portion of the left engine cowling starting to come loose. After obtaining clearance from air traffic control, he diverted to the Greeley/Weld County Airport. Shortly thereafter, the left cowling completely separated from the aircraft and struck the vertical stabilizer. The pilot reported no change in aircraft performance, but noted oil leaking from a cracked oil filler neck. He then made a normal and uneventful approach and landing at Greeley. Postaccident inspection disclosed substantial damage to the vertical stabilizer. The outboard cowling latches were found in the UNLOCKED position, and the inboard latches were in the LOCKED position. A portion of the cowling remained attached via the inboard latches. The pilot said he checked the cowling latches during his preflight inspection and they were all in the LOCKED position. Orange stripes had been painted across the latches to visually indicate LOCKED and UNLOCKED positions.