Security is of crucial importance to visible light communication (VLC) systems. In this paper, we propose and experimentally demonstrate a secure non-orthogonal multiple access (NOMA) VLC system with orthogonal frequency division multiplexing (OFDM) modulation, where the peak-to-average power ratio (PAPR) is also significantly reduced. Based on 2D chaotic map, the public key serves a two-fold purpose: to provide physical-layer security against eavesdropper, and to generate a set of phase-rotated candidate signals in the chaotic selected mapping (SLM) scheme where the signal with lowest PAPR is selected for transmission. The private keys further enhance the security and guarantee the privacy among the legitimate users via chaotic data scrambling. The experiment based on a direct current-biased optical OFDM (DCO-OFDM) VLC system with two legitimate users and one eavesdropper successfully verified the joint security enhancement and PAPR mitigation performance of the proposed scheme for NOMA VLC application.