  Ramanujan complexes are high dimensional simplical complexes generalizing
Ramanujan graphs. A result of Oh on quantitative property (T) for Lie groups
over local fields is used to deduce a Mixing Lemma for such complexes. As an
application we prove that non-partite Ramanujan complexes have 'high girth' and
high chromatic number, generalizing a well known result about Ramanujan graphs.
