Through advances in metamaterials-artificially engineered media with exotic properties, including negative refractive index(1-3)-the once fanciful invisibility cloak has now assumed a prominent place in scientific research(4-13). By extending these concepts to the temporal domain(14), investigators have recently described a cloak which hides events in time by creating a temporal gap in a probe beam that is subsequently closed up; any interaction which takes place during this hole in time is not detected(15). However, these results are limited to isolated events that fill a tiny portion of the temporal period, giving a fractional cloaking window of only about 10(-4) per cent at a repetition rate of 41 kilohertz (ref. 15)-which is much too low for applications such as optical communications. Here we demonstrate another technique for temporal cloaking, which operates at telecommunication data rates and, by exploiting temporal self-imaging through the Talbot effect, hides optical data from a receiver. We succeed in cloaking 46 per cent of the entire time axis and conceal pseudorandom digital data at a rate of 12.7 gigabits per second. This potential to cloak real-world messages introduces temporal cloaking into the sphere of practical application, with immediate ramifications in secure communications.