The effect of helicity on the Lagrangian velocity covariance UL(t) in isotropic, normally distributed turbulence is examined by computer simulation and by a renormalized perturbation expansion for UL(t). The first term of the latter represents Corrsin's (1959) conjecture (extrapolated to all t), which relates UL(t) to the Eulerian covariance and the distribution G(x, t) of fluid-element displacement. Truncation of the expansion at the first term yields the direct-interaction approximation for G(x, t). The expansion suggests that with or without helicity Corrsin's conjecture is valid as t → ∞ and that in either case UL(t) behaves asymptotically like $t^{-(r+\frac{3}{2})}$ if the spectrum of the Eulerian field varies like kr+2 at small wavenumbers. Corrsin's conjecture breaks down at small and moderate t if there is strong helicity while remaining accurate at all t in the mirror-symmetric case. Computer simulations for a frozen Eulerian field with spectrum confined to a thin spherical shell in k space indicate that strong helicity induces an increase in the Lagrangian correlation time by a factor of approximately three. Direct-interaction equations are constructed for the Lagrangian space-time covariance and the resulting prediction for UL(t) is compared with the simulations. The effect of helicity is well represented quantitatively by the direct-interaction equations for small and moderate t but not for large t. These frozen-field results imply good quantitative accuracy at all t in time-varying turbulence whose Eulerian correlation time is of the order of the eddy-circulation time. In turbulence with weak helicity, the directinteraction equations imply that the Lagrangian correlation of vorticity with initial velocity is more persistent than UL(t), by a substantial factor.