This paper presents a method for simulating chiral fermions on a lattice. The key idea is that a lattice theory of massive interacting fermions in 2n+1 dimensions can be used to simulate the behavior of massless chiral fermions in 2n dimensions if the fermion mass has a step function shape in the extra dimension. The massless states arise as zero-modes bound to the mass defect, and all doublers can be given large gauge invariant masses. The anomalies in the 2n-dimensional subspace are realized through charge flow into the extra dimension. The paper discusses the challenges of simulating chiral fermions on a lattice, noting that naive approaches suffer from the existence of doublers that render the theory vector-like instead of chiral. The paper also emphasizes the importance of correctly reproducing the anomalous Ward identities of the continuum theory and the necessity of correctly describing proton decay in a simulation of the standard model. The paper introduces a lattice model where chiral fermions in 2n dimensions can be simulated by Dirac fermions in 2n+1 dimensions with a space-dependent mass term. When there is a domain wall defect in the mass parameter, the lattice theory will exhibit massless chiral zero-modes bound to the 2n-dimensional domain wall, as well as doublers with the opposite chirality. The original 2n+1-dimensional theory is vector-like, so the doublers can be removed by means of a gauge-invariant Wilson term. The paper argues that whether or not these conditions can be met depends on an algebraic relation that ensures the 2n-dimensional gauge currents are exactly divergenceless. Global currents, however, may have anomalous divergences even in the regulated theory before taking the continuum limit, due to the role played by the extra dimension. The paper also discusses the resolution of a paradox regarding the anomaly in the effective 2n-dimensional theory. The resolution is that the massive fermion states that live off the domain walls do not entirely decouple, and so the effective theory is not truly 2n-dimensional. The Goldstone-Wilczek current is shown to be related to the Chern-Simons term induced by integrating out the massive fermion modes. The paper concludes that the 2n+1-dimensional lattice theory is vector-like at every step, and that the Wilson term can be used to eliminate the unwanted doublers. The paper also discusses the simulation of chiral gauge theories in background gauge fields and the possibility of simulating the standard model with this method. The paper concludes that the method can be used to simulate chiral fermions on a lattice, and that the proton decay can be understood in terms of the anomaly-free chiral gauge current.This paper presents a method for simulating chiral fermions on a lattice. The key idea is that a lattice theory of massive interacting fermions in 2n+1 dimensions can be used to simulate the behavior of massless chiral fermions in 2n dimensions if the fermion mass has a step function shape in the extra dimension. The massless states arise as zero-modes bound to the mass defect, and all doublers can be given large gauge invariant masses. The anomalies in the 2n-dimensional subspace are realized through charge flow into the extra dimension. The paper discusses the challenges of simulating chiral fermions on a lattice, noting that naive approaches suffer from the existence of doublers that render the theory vector-like instead of chiral. The paper also emphasizes the importance of correctly reproducing the anomalous Ward identities of the continuum theory and the necessity of correctly describing proton decay in a simulation of the standard model. The paper introduces a lattice model where chiral fermions in 2n dimensions can be simulated by Dirac fermions in 2n+1 dimensions with a space-dependent mass term. When there is a domain wall defect in the mass parameter, the lattice theory will exhibit massless chiral zero-modes bound to the 2n-dimensional domain wall, as well as doublers with the opposite chirality. The original 2n+1-dimensional theory is vector-like, so the doublers can be removed by means of a gauge-invariant Wilson term. The paper argues that whether or not these conditions can be met depends on an algebraic relation that ensures the 2n-dimensional gauge currents are exactly divergenceless. Global currents, however, may have anomalous divergences even in the regulated theory before taking the continuum limit, due to the role played by the extra dimension. The paper also discusses the resolution of a paradox regarding the anomaly in the effective 2n-dimensional theory. The resolution is that the massive fermion states that live off the domain walls do not entirely decouple, and so the effective theory is not truly 2n-dimensional. The Goldstone-Wilczek current is shown to be related to the Chern-Simons term induced by integrating out the massive fermion modes. The paper concludes that the 2n+1-dimensional lattice theory is vector-like at every step, and that the Wilson term can be used to eliminate the unwanted doublers. The paper also discusses the simulation of chiral gauge theories in background gauge fields and the possibility of simulating the standard model with this method. The paper concludes that the method can be used to simulate chiral fermions on a lattice, and that the proton decay can be understood in terms of the anomaly-free chiral gauge current.