James L. Van Uxem was a resident of Chicago, Illinois where he had a retail sporting goods shop from about 1885 until 1905. He sold firearms mostly but also carried some fishing tackle. Reels bearing his name are very rare. there are probably less than two dozen reels stamped with his name known to exist at the present time. Following are six nice marked examples  of the reels he sold.
Donadl P. Champion
ORCA member

The above reel is nickel plated brass in a 80 yard size. This example was made by John Kopf and being the only known example by this maker marked Van Uxem - Chicago.

The above reel was made by Montague City Rod Co. and is their four screw german silver model which their was top of the line reel. They made this reel as an answer to competition from the Kentucky reel makers. This reel is marked Jas. L. Van Uxem - Chicago and also marked with the name Geneva. The size marked under the foot is 13 1/2  which coresponds to the jeweled 80 yard model in the 1904 Montague catalog.

The above reel is Montague's raised gear case or "top hat" style german silver reel with jeweled oil caps. The size is marked 1 1/2 and also appears in the 1904 Montague catalog and is an 80 yard reel. This reel is also stamped Jas. L. Van Uxem - Chicago and marked with the name Geneva. Apparently he carried several different reels with the name Geneva.  

This is also a Montague reel in the raised gear case or "top hat" style. This reel is marked Jas. L. Van Uxem - Chicago and also with the name Grass Lake. It is an 80 yard example in nickel plated brass. It is not in as good a condition as the other reels shown here and hopefully I can upgrade it someday.

The above reel is marked Jas. L. Van Uxem - Chicago and Green Lake. It is an 80 yard nickel plated brass reel in the semi-Kentucky style. The drag is on the front and the click is on the back. This reel was also manufactured by the Montague City Rod Co.

This reel is marked Jas. L. Van Uxem - Chicago and also with the name Winona. It is a nickel plated brass 80 yard reel manufactured by Montague City Rod Co.  This concludes the examples I have of reels marked with James L. Van Uxem. There is one salt water example known to exist.