Since I seem to have made the quiz soporific with this one
, here's the rest of the answer: the southernmost naturally occurring palm tree is found right here in New Zealand - in fact I'm just a few metres from several as I type this. It's the nikau palm. The word "nikau" appears in several other Polynesian languages meaning coconut frond, so when Maori first arrived in New Zealand they probably named our nikau for its likeness to the coconut palms of their northern islands. This likeness may have led to some disappointment when coconuts failed to eventuate.
Nikau have been found as far south as 44° 18'S, while the fan palm grows at 43° 07' N.
More on both:
http://en.wikipedia.org/wiki/Chamaerops
http://en.wikipedia.org/wiki/Nikau
And for the linguistically inclined:
http://pollex.org.nz/entry/nii-kau/
Congratulations, Fbone, on your valiant answers! Please give the next question.