The feasibility of establishing and maintaining, in the presence of earth gravity, a planar laminar diffusion dame, with an only one-component velocity field, is examined. With purely gas-phase reactants, without phase transition, and without any intrusive surfaces for dame holding, such a dame would be especially amenable to theoretical analysis and diagnostic probing. Such a diffusion flame has advantages not achievable in a counterflow, which entails a two-component velocity field, and which becomes increasingly difficult to stabilize as the strain rate becomes smaller. In particular, we consider the diffusion-dominated case of an initially stagnant hydrogen/helium mixture, situated above an initially stagnant oxygen/argon mixture; the two mixtures are initially separated by a thin impervious barrier, which is rapidly removed, with minimal disturbance, so that ignition may ensue. The travel and temperature of the resulting planar diffusion flame may be analyzed as a one-dimensional Stefan problem; i.e., we may formulate and solve a problem in unsteady diffusion involving a moving planar interface (between fuel and oxidizer - the diffusion dame), the position of which is to be found in the course of solution. While we suggest how such a diffusion dame might be achieved in a practical apparatus of finite dimension, for simplicity we treat an idealized geometry that admits a selfsimilar solution, particularly conveniently pursued in a Lagrangian coordinate. According to results obtained from a tractable thin-dame formulation [with plausible, constant, but (as appropriate) nonunity values assigned to the ratios of the diffusive-transport coefficients], the chemical exothermicity associated with even a relatively weak flame would disrupt the initially stable stratification of the density in earth gravity. Thus, achievement of a planar, unidirectional-flow diffusion flame seems feasible only in microgravity.