Mentioned by Pliny in his Natural History(1) as being ornamental and having medicinal properties, the True Date Palm (Phoenix dactylifera), which was normally restricted to semi-deserts(2) was able to grow in Italy but was usually stunted and would not fruit(3)
bibliography
(1)Pliny's Natural History; XIII, 6,26
(2)Oxford Encyclopedia of trees of the world; p258
(3)Ancient Roman Gardens; Linda Farrar;1998; p141