  We present a technique which utilizes unitarity and collinear limits to
construct ansatze for one-loop amplitudes in gauge theory. As an example, we
obtain the one-loop contribution to amplitudes for $n$ gluon scattering in
$N=4$ supersymmetric Yang-Mills theory with the helicity configuration of the
Parke-Taylor tree amplitudes. We prove that our $N=4$ ansatz is correct using
general properties of the relevant one-loop $n$-point integrals. We also give
the ``splitting amplitudes'' which govern the collinear behavior of one-loop
helicity amplitudes in gauge theories.
