The Drosophila larva executes a stereotypical exploratory routine that appears to consist of stochastic alternation between straight peristaltic crawling and reorientation events through lateral bending. We present a model of larval mechanics for axial and transverse motion over a planar substrate, and use it to develop a simple, reflexive neuromuscular model from physical principles. The mechanical model represents the midline of the larva as a set of point masses which interact with each other via damped translational and torsional springs, and with the environment via sliding friction forces. The neuromuscular model consists of: 1. segmentally localised reflexes that amplify axial compression in order to counteract frictive energy losses, and 2. long-range mutual inhibition between reflexes in distant segments, enabling overall motion of the model larva relative to its substrate. In the absence of damping and driving, the mechanical model produces axial travelling waves, lateral oscillations, and unpredictable, chaotic deformations. The neuromuscular model counteracts friction to recover these motion patterns, giving rise to forward and backward peristalsis in addition to turning. Our model produces spontaneous exploration, even though the nervous system has no intrinsic pattern generating or decision making ability, and neither senses nor drives bending motions. Ultimately, our model suggests a novel view of larval exploration as a deterministic superdiffusion process which is mechanistically grounded in the chaotic mechanics of the body. We discuss how this may provide new interpretations for existing observations at the level of tissue-scale activity patterns and neural circuitry, and provide some experimental predictions that would test the extent to which the mechanisms we present translate to the real larva.