A variational coarse-mesh technique is developed for the solution of the multigroup neutron transport equation in one-dimensional reactor lattices. In contrast to conventional nodal lattice applications that discretize diffusion theory and use node homogenized cross sections, the methods used here retain the spatial dependence of the cross sections and instead employ an alternative flux representation, a slowly modulated pin cell flux, that allows the neutron transport equation to be cast into a form whose solution has a relatively slow spatial and angular variation and that can be accurately described with relatively few variables. This alternative flux representation and the stationary property of a variational principle define a class of coarse-mesh discretizations of transport theory that are capable of achieving order-of-magnitude reductions of eigenvalue and pointwise scalar flux errors compared with diffusion theory while retaining the relatively low cost of diffusion theory.