  This paper introduces a variant of the impartial combinatorial game nim,
called tree nim, as well as a particular case of tree nim called tripod nim. A
certain existence-uniqueness result and a periodicity result are proven about
the distribution of $\mathcal{P}$-positions and Grundy values in tree nim.
Tripod nim is associated to a family of arrays similar to those which arise in
the study of sequential compound games. Using these arrays, a partial analysis
is given for tripod nim. Conjectures relating to the periods of the rows of
these arrays are put forward.
