For a time, years back, Kimber was taking clean 96's, lowering the bolt handle, drilling and tapping em, and generally sportsterizing them, including a Ram-Line plastic stock. Does your rifle have a wood grain plastic stock? I do not know anything about the markings or chamberings of these Kimbers, but it looks like it could be one of them. But yea, if not clearly marked, have a chamber cast done, or at least try a set of 6.5X55 "go"/"no go" gauges. Any decent gunsmith can do either.
Larry