This study proposes a tractable approach to analyze the physical-layer security in the downlink of a multi-tier heterogeneous cellular network. This method is based on stochastic geometry, has low computational complexity, and uses the two-dimensional Poisson point process to model the locations of K-tier base stations and receivers, including those of legitimate users and eavesdroppers. Then, the achievable secrecy rates for an arbitrary user are determined and the upper and lower bounds of secrecy coverage probability derived on the condition that cross-tier interference is the main contributor to aggregate interference. Finally, our analysis results reveal the innate connections between information-theoretic security and the spatial densities of legitimate and malicious nodes.