The pure rotational spectrum of the molecular ion VCl+ (X (4)Sigma(-)) has been recorded from 274 to 419 GHz using a combination of millimeter direct absorption and velocity modulation spectroscopy. This study is the first spectroscopic measurement of this species in the laboratory, which has also enabled the determination of the ground state term, (4)Sigma(-). VCl+ was produced in an AC discharge of VCl4 and argon. Fifteen and eleven rotational transitions were recorded for the (VCl+)-Cl-35 and (VCl+)-Cl-37 isotopologues, respectively. The fine structure splittings of the (4)Sigma(-) state were found to deviate significantly from a case (b) pattern. Specifically, spin components from adjacent rotational transitions were found to overlap in frequency. Unusual vanadium hyperfine splittings were also observed in the VCl+ spectra; the expected vanadium octet was clearly present for the F-2 and F-3 spin components but was partially collapsed and reversed in frequency ordering in the F-1 and F-4 cases. The data were analyzed in a global fit, and rotational, fine structure, and hyperfine constants were determined. For VCl+, the values of both the spin-spin and spin-rotation parameters are extremely large, as were the third-order hyperfine and spin-rotation terms, b(s) and gamma(s). For example, the spin-spin constant is lambda = 417 900(22 700) MHz, while gamma = 6567(51) MHz. The values of these constants indicate a high density of excited electronic states close to the ground state, which contribute to second and third-order spin-orbit coupling. The hyperfine constants suggest a sigma(1)pi(2) electron configuration, as opposed to sigma(1)delta(2), as found in VS and VO. The bond length of VCl+, r(0) = 2.119(2) angstrom, is shorter than that of VCl by 0.1 angstrom, which has r(0) = 2.219 angstrom. The decrease in bond length is attributed to an increase in the electrostatic attraction between V2+ and Cl-, as opposed to V+ and Cl- for VCl.