I was told there ware some massive tax restrictions that made exporting complete watches to the United States very costly. As a consequence, many manufacturers founded subsidiaries in the States that manufactured the cases, so the imported movements were encased locally. UN had its subsidiary in New York, so the stamp on the inner side of the case appears to be genuine. The company name was "UN chronometer Co.", so the watch itself was not necessarily a certified chronometer.
The movement seems to be a 9.25''' AS 1320, or the larger AS 1364. Ulysse Nardin did not make own wristwatch movements at that time, only pocket watches. So the movements used were supplied from dedicated movement manufacturers like A. Schild, ETA, and many others.
Marcus