This paper presents a method for constructing one-loop amplitudes in gauge theory using unitarity and collinear limits. The method is applied to 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. The authors prove that their N = 4 ansatz is correct using general properties of the relevant one-loop n-point integrals. They also provide "splitting amplitudes" that govern the collinear behavior of one-loop helicity amplitudes in gauge theories. The paper discusses the use of collinear limits and unitarity to construct ansätze for one-loop amplitudes. The collinear limit of an n-point amplitude reduces to a sum of (n-1)-point amplitudes multiplied by known, singular functions — "splitting amplitudes". The tree-level splitting amplitudes are related to the leading-order polarized Altarelli-Parisi coefficients. The loop-level splitting functions can be extracted from the collinear behavior of one-loop five-parton amplitudes. The authors use a bootstrap approach to construct ansätze for n-point one-loop amplitudes, starting with known one-loop lower-point results. The second constraint is perturbative unitarity. The authors apply the Cutkosky rules to determine the absorptive parts (cuts) of the amplitude in all possible channels. The cut amplitude can be written as a tree amplitude on one side of the cut, multiplied by a tree amplitude on the other side of the cut, with the loop integral replaced by an integral over the phase space of the particles crossing the cut. These cuts are generally simpler to evaluate than the full amplitude. The authors show that the cuts uniquely determine the amplitude, proving the correctness of the ansatz obtained via the unitary-collinear bootstrap. The paper also discusses the use of supersymmetry to simplify the calculation of amplitudes. The N = 4 super-Yang-Mills results can be used as part of the computation of the corresponding n-gluon helicity amplitude in QCD, where gluons and quarks circulate in the loop. The authors show that the N = 4 super-Yang-Mills results are one of the three components of a QCD calculation organized in this manner. The simplicity of the N = 4 results suggests that the expressions for amplitudes (a) and (b) should be relatively simple, while the remaining scalar loop computation (c) is much easier than a direct gluon (or quark) loop computation. The paper also discusses the use of supersymmetry to cancel divergences in the calculation of amplitudes. The N = 4 supersymmetric theory has further cancellations that allow the authors to prove that the process outlined generates the correct amplitude. The authors use a "gedanken calculation" of the loop amplitude using either supersThis paper presents a method for constructing one-loop amplitudes in gauge theory using unitarity and collinear limits. The method is applied to 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. The authors prove that their N = 4 ansatz is correct using general properties of the relevant one-loop n-point integrals. They also provide "splitting amplitudes" that govern the collinear behavior of one-loop helicity amplitudes in gauge theories. The paper discusses the use of collinear limits and unitarity to construct ansätze for one-loop amplitudes. The collinear limit of an n-point amplitude reduces to a sum of (n-1)-point amplitudes multiplied by known, singular functions — "splitting amplitudes". The tree-level splitting amplitudes are related to the leading-order polarized Altarelli-Parisi coefficients. The loop-level splitting functions can be extracted from the collinear behavior of one-loop five-parton amplitudes. The authors use a bootstrap approach to construct ansätze for n-point one-loop amplitudes, starting with known one-loop lower-point results. The second constraint is perturbative unitarity. The authors apply the Cutkosky rules to determine the absorptive parts (cuts) of the amplitude in all possible channels. The cut amplitude can be written as a tree amplitude on one side of the cut, multiplied by a tree amplitude on the other side of the cut, with the loop integral replaced by an integral over the phase space of the particles crossing the cut. These cuts are generally simpler to evaluate than the full amplitude. The authors show that the cuts uniquely determine the amplitude, proving the correctness of the ansatz obtained via the unitary-collinear bootstrap. The paper also discusses the use of supersymmetry to simplify the calculation of amplitudes. The N = 4 super-Yang-Mills results can be used as part of the computation of the corresponding n-gluon helicity amplitude in QCD, where gluons and quarks circulate in the loop. The authors show that the N = 4 super-Yang-Mills results are one of the three components of a QCD calculation organized in this manner. The simplicity of the N = 4 results suggests that the expressions for amplitudes (a) and (b) should be relatively simple, while the remaining scalar loop computation (c) is much easier than a direct gluon (or quark) loop computation. The paper also discusses the use of supersymmetry to cancel divergences in the calculation of amplitudes. The N = 4 supersymmetric theory has further cancellations that allow the authors to prove that the process outlined generates the correct amplitude. The authors use a "gedanken calculation" of the loop amplitude using either supers