This paper investigates the secrecy performance of the multiple-input single-output (MISO) visible light communication (VLC) wiretap channel. The considered system model comprises three nodes: a transmitter (Alice) equipped with multiple fixtures of LEDs, a legitimate receiver (Bob) and an eavesdropper (Eve), each equipped with one photo-diode (PD). The VLC channel is modeled as a real-valued amplitude-constrained Gaussian channel. Eve is assumed to be randomly located in the same area as Bob. Due to this, artificial noise (AN)-based beamforming is adopted as a transmission strategy in order to degrade Eve’s signal-to-noise ratio (SNR). Assuming discrete input signaling, we derive an achievable secrecy rate in a closed-form expression as a function of the beamforming vectors and the input distribution. We investigate the average secrecy performance of the system using stochastic geometry to account for the location randomness of Eve. We also adopt the truncated discrete generalized normal (TDGN) as a discrete input distribution. We present several examples through which we confirm the accuracy of the analytical results via Monte Carlo simulations. The results also demonstrate that the TDGN distribution, albeit being not optimal, yields performance close to the secrecy capacity.