We present evidence for chaotic dynamics within the spin-down rates of 17 pulsars originally presented by Lyne et al . Using techniques that allow us to re-sample the original measurements without losing structural information , we have searched for evidence of a strange attractor in the time series of frequency derivatives for each of the 17 pulsars . We demonstrate the effectiveness of our methods by applying them to a component of the Lorenz and Rössler attractors that were sampled with similar cadence to the pulsar time series . Our measurements of correlation dimension and Lyapunov exponent show that the underlying behaviour appears to be driven by a strange attractor with approximately three governing non-linear differential equations . This is particularly apparent in the case of PSR B1828 - 11 where a correlation dimension of 2.06 \pm 0.03 and a Lyapunov exponent of ( 4.0 \pm 0.3 ) \times 10 ^ { -4 } inverse days were measured . These results provide an additional diagnostic for testing future models of this behaviour .