An eruption along a 2.5 km-long rhyolitic dyke at Krafla volcano, northern Iceland during the last glacial period formed a ridge of obsidian (Hrafntinnuhryggur). The ridge rises up to 80 m above the surrounding land and is composed of a number of small-volume lava bodies with minor fragmental material. The total volume is <0.05 km3. The lava bodies are flow- or dome-like in morphology and many display columnar-jointed sides typical of magma-ice interaction, quench-fragmented lower margins indicative of interaction with meltwater and pumiceous upper surfaces typical of subaerial obsidian flows. The fragmental material compromises poorly-sorted perlitic quench hyaloclastites and poorly-exposed pumiceous tuffs. Lava bodies on the western ridge flanks are columnar jointed and extensively hydrothermally altered. At the southern end of the ridge the feeder dyke is exposed at an elevation ~95 m beneath the ridge crest and flares upwards into a lava body. Using the distribution of lithofacies, we interpret that the eruption melted through ice only 35-55 m thick, which is likely to have been dominated by firn. Hrafntinnuhryggur is therefore the first documented example of a rhyolitic fissure eruption beneath thin ice/firn. The eruption breached the ice, leading to subaerial but ice/firn-contact lava effusion, and only minor explosive activity occurred. The ridge appears to have been well-drained during the eruption, aided by the high permeability of the thin ice/firn, which appears not to have greatly affected the eruption mechanisms. We estimate that the eruption lasted between 2 and 20 months and would not have generated a significant jökulhlaup (<70 m3s-1).