The spin part of angular momentum of the electromagnetic field is known since the 1990's to be a separately conserved quantity. Cameron et al. introduced the helicity array, a non-covariant analog of Lipkin's zilch tensor, which expresses the hierarchy of conservation laws including helicity, spin, as well as the spin-flux or infra-zilch. In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced. The conservation laws arising from the helicity array can be obtained from the helicity tensor. The Lorentz covariance of the helicity tensor is in contrast to previous formulations of the helicity hierarchy of conservation laws, which required the non-Lorentz covariant transverse gauge. The helicity tensor is shown to arise as a Noether current for a variational symmetry of a duality-symmetric Lagrangian for Maxwell theory.