We present interferometric HI observations of six double-disc stellar counterrotator (2$sigma$) galaxies from the Atlas3D sample. Three are detected in HI emission; two of these are new detections. NGC 7710 shows a modestly asymmetric HI disc, and the atomic gas in PGC 056772 is centrally peaked but too poorly resolved to identify the direction of rotation. IC 0719, the most instructive system in this study, shows an extended, strongly warped disc of 43 kpc diameter, with a faint tail extending towards its neighbor IC 0718. The gas has likely been accreted from this external source during an encounter whose geometry directed the gas into misaligned retrograde orbits (with respect to the primary stellar body of IC 0719). In the interior, where dynamical time-scales are shorter, the HI has settled into the equatorial plane forming the retrograde secondary stellar disc. This is the first direct evidence that a double-disc stellar counterrotator could be formed through the accretion of retrograde gas. However, the dominant formation pathway for the formation of $2sigma$ galaxies is still unclear. The Atlas3D sample shows some cases of the retrograde accretion scenario and also some cases in which a scenario based on an unusually well-aligned merger is more likely.
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