Summary: Contemporary writers often claim that chaos theory explains the thermodynamic arrow of time. This paper argues that such claims are mistaken, on two levels. First, they underestimate the difficulty of extracting asymmetric conclusions from symmetric theories. More important, however, they misunderstand the nature of the puzzle about the temporal asymmetry of thermodynamics, and simply address the wrong issue. Both of these are old mistakes, but mistakes which are poorly recognised, even today. This paper aims to lay bare the mistakes in their classical (pre chaos theory) manifestations, in order to make it clear that chaos theory cannot possibly do better.