  6D maximal super Yang-Mills on-shell amplitudes are formulated in superspace
using 6 dimensional twistors. The 3,4,5-point tree amplitudes are obtained by
supersymmetrizing their bosonic counterparts and confirmed through the BCFW
construction. In contrast to 4D this superspace is non-chiral, reflecting the
fact that one cannot differentiate MHV from $\bar{{\rm MHV}}$ in 6D. Combined
with unitarity methods, this superspace should be useful for the study of
multi-loop D dimensional maximal super Yang-Mills and gravity amplitudes.
Furthermore, the non-chiral nature gives a natural framework for an off-shell
construction. We show this by matching our result with off-shell D=4 N=4 super
Yang-Mills amplitudes, expressed in projective superspace.
