We present a detailed study of the dielectric and charge transport properties of the antiferromagnetic cubic spinel HgCr 2 S 4 . Similar to the findings in ferromagnetic CdCr 2 S 4 , the dielectric constant of HgCr 2 S 4 becomes strongly enhanced in the region below 60 -80 K, which can be ascribed to polar relaxational dynamics triggered by the onset of ferromagnetic correlations. In addition, the observation of polarization hysteresis curves indicates the development of ferroelectric order below about 70 K. Moreover, our investigations in external magnetic fields up to 5 T reveal the simultaneous occurrence of magnetocapacitance and magnetoresistance of truly colossal magnitudes in this material.PACS numbers: 75.80.+q, 77.22.Gm The detection of c olossal magnetoresistance in a number of perovskite-related manganites [1] maybe was the most notable discovery in solid state physics since the emergence of high-T c superconductors. Very recently another "colossal" effect with tremendous prospects for applications in modern microelectronics attracted considerable attention: In several, partly quite different materials an extremely strong coupling of magnetic and dielectric properties, termed "magnetocapacitive" or "magnetoelectric" effect, was found [2,3]. Among these, the cubic spinel CdCr 2 S 4 stands out by showing simultaneous ferromagnetic (FM) and relaxor ferroelectric behavior [3] and by setting a record value of the magnetocapacitive effect with an increase of the dielectric constant ε' of up to 3000% in a magnetic field of 10 T [4]. At the FM transition at T c ≈ 84 K, the dielectric constant shows a strong increase, which was ascribed to a speeding up of relaxational dynamics under the formation of magnetic order [ 4]. However, c learly the microscopic origin of the extraordinary behavior of CdCr 2 S 4 is far from being understood. A similar, but weaker effect was recently reported in isostructural CdCr 2 Se 4 [5] exhibiting FM order below T c ≈ 125 K. In the present letter, we provide dielectric data on HgCr 2 S 4 , which in contrast to CdCr 2 S 4 does not show any long-range FM order but exhibits a complex antiferromagnetic (AFM) type of order below 22 K [ 6]. Nevertheless, it shows a colossal magnetocapacitance (CMC) of even larger amplitude than in CdCr 2 S 4 and, m ost remarkably, the simultaneous occurrence of colossal magnetoresistance (CMR). In addition, our experiments indicate that in HgCr 2 S 4 , similar to our findings in CdCr 2 S 4 , short range ferroelectric order develops at low temperatures.All measurements were performed on single crystals of HgCr 2 S 4 , grown by chemical transport. Measurements with silver paint and sputtered gold contacts applied to opposite sides of the samples were performed. Details on crystal preparation and experimental methods are given in Refs. [3,6]. A thorough characterization of the magnetic properties of HgCr 2 S 4 [6] revealed an AFM state with non-collinear spin configuration below 22 K [ 7]. In moderate external magnetic fields up to 0.5 T, the AFM transi...