We present new high-resolution neutral hydrogen (H I) images of the Galactic supershell GSH 242-03+37. These data were obtained with the Parkes Radiotelescope as part of the Galactic All-Sky Survey (GASS). GSH 242-03+37 is one of the largest and most energetic H I supershells in the Galaxy, with a radius of 565 ± 65 pc and an expansion energy of 3 × 10 53 ergs. Our images reveal a complicated shell with multiple chimney structures on both sides of the Galactic plane. These chimneys appear capped by narrow filaments about 1.6 kpc above and below the Galactic midplane, confirming structures predicted in simulations of expanding supershells. The structure of GSH 242-03+37 is extremely similar to the only other Galactic supershell known to have blown out of both sides of the plane, GSH 277+00+36. We compare the GASS H I data with X-ray and Ha images, finding no strong correlations.