You can use this site to see where the name was most common in Ireland in the mid 1850s. In general it was found in the counties of Ulster. If the family were Presbyterian then that would not be surprising. If so, chances are they are descended from Scots settlers who moved to Ireland in the 1600s.
http://www.irishtimes.com/ancestor/surname/Chambers found all over Ireland but in the main again in Ulster.