We report the first results of abinitio relativistic correlation calculation of the effective electric field on the electron, Eeff, in the ground state of the HI+ cation. This value is required for interpretation of the suggested experiment on the search for the electron electric dipole moment. The generalized relativistic effective core potential, Fock-space relativistic coupled cluster with single and double cluster amplitudes (RCC-SD), and spin-orbit direct configuration interaction (SODCI) methods are used, followed by nonvariational one-center restoration of the four-component wave function in the iodine core. The RCC-SD value is Eeff=0.345×1024Hz/ecm and SODCI study gives Eeff=0.336×1024Hz/ecm (our final value). The structure of chemical bonding in HI+ is clarified, and a significant deviation of our value from that of Ravaine etal. [Phys. Rev. Lett. 94, 013001 (2005)PRLTAO0031-900710.1103/ PhysRevLett.94.013001] is explained.