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Airborne Laser Swath Mapping instrument technology and subsequent algorithm advances have made it possible over the last few years to map the Earth's surface and land cover at unprecedented resolution. The ability of Airborne Laser Swath Mapping technology to densely sample ground elevations beneath forest canopies is particularly important because forested watersheds have traditionally been difficult to study with remote sensing techniques. The extraction of stream networks from digital elevation models (DEMs) plays a fundamental role in modelling local and spatially distributed hydrological processes. Our approach, based on an encoding of mathematical morphological operators, is shown to systematically and accurately extract stream channel locations, forms and incipient incisions in a forested watershed. The accuracy of the method is verified using a set of error measures over simulated terrain and also over real terrain where the site was manually surveyed.