We introduce a model for translational molecular motors to demonstrate that a multivalent catalytic walker with flexible, uncoordinated legs can transform the free energy of surface-bound substrate sites into mechanical work and undergo biased, superdiffusive motion, even in opposition to an external load force. The walker in the model lacks any inherent orientation of body or track, and its legs have no chemomechanical coupling other than the passive constraint imposed by their connection to a common body. Yet, under appropriate kinetic conditions, the walker’s motion is biased in the direction of unvisited sites, which allows the walker to move nearly ballistically away from the origin as long as a local supply of unmodified substrate sites is available. The multivalent random walker model is mathematically formulated as a continuous-time Markov process and is studied numerically. We use Monte Carlo simulations to generate ensemble estimates of the mean squared displacement and mean work done for this nonergodic system. Our results show that a residence time bias between visited and unvisited sites leads to superdiffusive motion over significant times and distances. This mechanism can be used to adapt any enzyme-substrate system with appropriate kinetics for use as a functional chemical implementation of a molecular motor, without the need for structural anisotropy or conformationally mediated chemomechanical coordination.