We developed a high-performance methane gas sensor based on a $SnO_2$ hollow hemisphere array structure of nano-thickness. The sensor structures were fabricated by sputter deposition of Sn metal over an array of polystyrene spheres distributed on a planar substrate, followed by an oxidation process to oxidize the Sn to $SnO_2$ while removing the polystyrene template cores. The surface morphology and structural properties were examined by scanning electron microscopy. An optimization of the structure for methane sensing was also carried out. The effects of oxidation temperature, film thickness, gold doping, and morphology were examined. An impressive response of ~220% was observed for a 200 ppm concentration of $CH_4$ gas at an operating temperature of $400^{circ}C$ for a sample fabricated by 30 sec sputtering of Sn, and oxidation at $800^{circ}C$ for 2 hr in air. This high response was enabled by the open structure of the hemisphere array thin films.