"An uneasy idea persists that gotten is improper," says Roy H. Copperud in A Dictionary of Usage and Style. "Efforts to avoid got by substituting obtained or any other word the writer must strain after are misspent."
Gotten has been in continuous use for about seven hundred years, though it all but disappeared from England in the eighteenth century. "In Great Britain got is the only form of the participle used and the older form gotten is considered archaic," says Bergen and Cornelia Evans's Dictionary of Contemporary American Usage. "In the United States gotten is still the preferred form of the participle when it is used with have to express a completed action."