We investigate the properties of spinel structure ZnCr2Te4 as a candidate cubic material for giant transport anisotropy. We find that this cubic spinel ZnCr2Te4 phase is a ferromagnetic semimetal and that it is metastable, with an enthalpy only slightly above that of the competing phases, ZnTe and Cr2Te3. The Fermi surface is derived from bands of opposite spin that cross very close to the Fermi level. This results in an unusual situation where the interplay of spin orbit coupling and magnetism substantially reconstructs the Fermi surface in a way that depends on magnetization direction. This leads to a prediction of unusual anisotropic transport behavior in a cubic material. For magnetization along [001], we find σzz(20 K)/σxx(20 K) = 1.27. This is a large anisotropy for a cubic material. At a temperature of 200 K the anisotropy decreases to σzz(200 K)/σxx(200 K) = 1.11 presuming the ferromagnetism remains intact. For the [111] magnetization direction, the conductivity anisotropy is low at 20 K, but increases with temperature to a value σ∥(200 K)/σ⊥(200 K) = 1.10 at 200 K, where ∥ and ⊥ denote conductivity along the [111] magnetization direction, and perpendicular to it, respectively.