An Etymological Dictionary of the German Language/Gaden
Gaden, Gadem, m. and n., ‘room, cottage, storey,’ from MidHG. and MidLG. gaden, gadem, n., ‘house containing one room only,’ then generally ‘apartment, chamber,’ OHG. gadum, gadaum, n.; orig. a merely UpG. word, which found its way, however, even into LG. Akin to Goth. *gatm (from ga- and tmo-, the latter related to Gr. δόμος, μεσό-δμη, and HG. Zimmer)?. Less probably allied to AS. geat, E. gate (comp. Du. gat, ‘opening,’ under Gasse). At all events, the connection with Gr. χιτών, ‘garment,’ is impossible.