We propose an indoor multiple-input, single-output (MISO) visible light communication (VLC) system involving massive, i.e., very large, number of light-emitting diodes (LEDs). Thousands of low-intensity LEDs are arranged in a two-dimensional array occupying the entire area of the ceiling to provide uniform illumination. We exploit the excessive spatial degrees of freedom offered by the large number of LEDs to achieve secure communications to the intended receivers, at the physical layer, without precise information about the location or channel gain of potential eavesdroppers. We design the weights (magnitude and sign) of the array elements, i.e., LEDs, to shape the overall pattern of the array and steer its main lobe(s) towards the intended receiver(s), while achieving arbitrarily small signal levels everywhere else inside the room. We formulate the pattern synthesis problem as a linear program with moderate complexity, and characterize the worst-case secrecy rates. We verify the illumination as well as the communication performance of the proposed setup via numerical results.