An ostensible chicken-gopher hybrid was reported on page 7, column 7, of the December 3, 1913, issue of the Willmar Tribune, a newspaper published in Willmar, Minnesota (source). The story originally ran in the Tyler Journal, published in Tyler, Minnesota. The following is a transcript of the report:
A hen with a gopher head in the gopher state is something to take notice of.
Mr. Lemon is dickering with the managers of several museums in the largest cities of the United States. As a curiosity the hen is worth considerable and the chances are that some museum will have the hen on exhibit within a short time.—Tyler Journal.
There are many kinds of gophers, but given the location of the reported event (Tyler, Minnesota), the rodent in question would almost certainly be Geomys bursarius, the Plains Pocket Gopher. According to Wikipedia, these rodents spend 72 percent of their time underground, but do emerge in search of food or mates.
A similarly composite rodent-headed chicken, but in this case with the head of a rat, was briefly described on page 4, column 2, of the April 17, 1915, issue of the Scott County Kicker, a newspaper published in Benton, Missouri (source):
Congenital blindness seems to be fairly frequent in distant hybrids, perhaps due to the disruption of ordinary developmental processes. Such hybrids are often born without eyes. Cyclopean births also appear to occur at elevated rates.