Must quibble about the unbroken lineage claim. The Massachusetts Army National Guard holds the title, as listed in the Department of the Army Historical Services Office from which the following comes:
the first muster of the East Regiment took place in Salem, Massachusetts. The National Guard continues its historic mission of providing units for the first-line defense of the nation. The 101st Engineer Battalion, Massachusetts Army National Guard, continues the East Regiment's proud heritage of 350 years of service.