The arm patch is the style of a Navy Chief’s chevron. Single star would be a Senior Chief.
Two things regarding that interpretation:
1. The stars on senior and master chiefs' insignias are located above the crow. (The area between the rocker and top chevron is used for the rating designator.)
2. The senior and master chief ranks didn't come into existence until 1958.
The Senior and Master Chief rates were added much later than that date, just a few years before I enlisted (1961). And the star(s) go above the eagle. The star in this case is in the place where the rating badge would be (crossed anchors = boatswain's mate, gear = engineman, crossed cannons - gunner's mate, etc.). It may be decoration.