  Let $n$ points be placed independently in $d-$dimensional space according to
the standard $d-$dimensional normal distribution. Let $d_n$ be the longest edge
length for the nearest neighbor graph on these points. We show that \[\lim_{n
\rar \infty} \frac{\sqrt{\log n} d_n}{\log \log n} = \frac{d}{\sqrt{2}}, \qquad
d \geq 2, {a.s.} \]
