We have used deep near-infrared observations with adaptive optics to discover a distributed population of low-mass protostars within the filamentary Infrared Dark Cloud G34.43+00.24. We use maps of dust emission at multiple wavelengths to determine the column density structure of the cloud. In combination with an empirically-verified model of the magnitude distribution of background stars, this column density map allows us to reliably determine overdensities of red sources that are due to embedded protostars in the cloud. We also identify protostars through their extended emission in K-band which comes from excited H2 in protostellar outflows or reflection nebulosity. We find a population of distributed low-mass protostars, suggesting that low-mass protostars may form earlier than, or contemporaneously with, high-mass protostars in such a filament. The low-mass protostellar population may also produce the narrow linewidth SiO emission observed in some clouds without high-mass protostars. Finally, we use a molecular line map of the cloud to determine the virial parameter per unit length along the filament and find that the highest mass protostars form in the most bound portion of the filament, as suggested by theoretical models.