High-speed visible light communication (VLC) is a complementary technology to conventional radio frequency communication in wireless networks. One of the essential traits of VLC systems is the ability to provide wireless communication and illumination seamlessly. High-speed VLC systems use high-power LEDs as transmitters in their access points (APs). In real-world deployments, overlapping light beams from multiple APs are necessary to avoid unlit areas. However, overlapping light beams could cause interference in each other's communication at the receiver; hence APs must synchronise their communication. This paper presents Harmony, a time synchronisation system for VLC APs to synchronise their transmissions. Internally, Harmony uses synchronous transmissions in the infrared frequency spectrum to reach nodes over multiple hops. The evaluation of a prototype implementation of Harmony on a small-scale testbed shows that it can synchronise nodes up to nine hops with a maximum error of a few 100s of nanoseconds. While the enduring work on high-speed VLC systems primarily focuses on improving the performance of individual APs, Harmony provides an infrastructure for enhancing system-wide performance.