Nanostructures are known to be exquisitely sensitive to the chemical environment and offer ultra-high sensitivity for gas-sensing. However, the fabrication and operation of devices that use individual nanostructures for sensing is complex, expensive and suffers from poor reliability due to contamination and large variability from sample-to-sample. By contrast, conventional solid-state and conducting-polymer sensors offer excellent reliability but suffer from reduced sensitivity at room-temperature. Here we report a macro graphene foam-like three-dimensional network which combines the best of both worlds. The walls of the foam are comprised of few-layer graphene sheets resulting in high sensitivity; we demonstrate parts-per-million level detection of NH3 and NO2 in air at room-temperature. Further, the foam is a mechanically robust and flexible macro-scale network that is easy to contact (without Lithography) and can rival the durability and affordability of traditional sensors. Moreover, Joule-heating expels chemisorbed molecules from the foam's surface leading to fully-reversible and low-power operation.