  We show that one-loop amplitudes in massless gauge theories can be determined
from single cuts. By cutting a single propagator and putting it on-shell, the
integrand of an n-point one-loop integral is transformed into an (n+2)-particle
tree level amplitude. The single-cut approach described here is complementary
to the double or multiple unitarity cut approaches commonly used in the
literature. In common with these approaches, if the cut is taken in four
dimensions, one finds only the cut-constructible parts of the amplitude, while
if the cut is in D=4-2 epsilon dimensions, both rational and cut-constructible
parts are obtained. We test our method by reproducing the known results for the
fully rational all-plus and mostly-plus QCD amplitudes
A^{(1)}_4(1^+,2^+,3^+,4^+) and A^{(1)}_5(1^+,2^+,3^+,4^+,5^+). We also rederive
expressions for the scalar loop contribution to the four-gluon MHV amplitude,
A_4^{(1,N=0)}(-,-,+,+) which has both cut-constructible and rational
contributions, and the fully cut-constructible n-gluon MHV amplitude in N=4
Supersymetric Yang-Mills, A_4^{(1,N=4)}(-,-,+,...,+).
