As a highly complex and integrated cyber-physical system, modern power grids are exposed to cyberattacks. False data injection attacks (FDIAs), specifically, represent a major class of cyber threats to smart grids by targeting the measurement data's integrity. Although various solutions have been proposed to detect those cyberattacks, the vast majority of the works have ignored the inherent graph structure of the power grid measurements and validated their detectors only for small test systems with less than a few hundred buses. To better exploit the spatial correlations of smart grid measurements, this paper proposes a deep learning model for cyberattack detection in large-scale AC power grids using Chebyshev Graph Convolutional Networks (CGCN). By reducing the complexity of spectral graph filters and making them localized, CGCN provides a fast and efficient convolution operation to model the graph structural smart grid data. We numerically verify that the proposed CGCN based detector surpasses the state-of-the-art model by 7.86 in detection rate and 9.67 in false alarm rate for a large-scale power grid with 2848 buses. It is notable that the proposed approach detects cyberattacks under 4 milliseconds for a 2848-bus system, which makes it a good candidate for real-time detection of cyberattacks in large systems.