The τ Herculid meteor shower has not shown any appreciable activity since 1930. However, it is associated with Comet 73P/Schwassmann-Wachmann 3, a Jupiter-family comet that split in 1995. The fragments will pass near the Earth on 2006 May 13, and could produce an outburst of the τ Herculid shower. However, by considering both meteoroids released during the splitting event and on previous perihelion passages back to 1801, we find no evidence for enhanced activity from this shower in 2006. This is a result partly of the dynamics of the parent comet, which suffers frequent close encounters with Jupiter, and partly of the location and timing of the splitting event, which produces a distribution of meteoroids that does not approach the Earth particularly closely. In fact, we show that the 1930 observations date from one of the few expected appearances of the τ Herculid shower and predict that detectable activity will be produced in 2022 and 2049.