We test the parallaxes reported in the Gaia first data release using the sample of eclipsing binaries with accurate, empirical distances from Stassun & Torres (2016, arXiv:1609.02579). We find an average offset of -0.25+/-0.05mas in the sense of the Gaia parallaxes being too small (i.e., the distances too long). The offset does not depend strongly on obvious parameters such as color or brightness. However, we find with high confidence that the offset may depend on ecliptic latitude: the mean offset is -0.38+/-0.06mas in the ecliptic north and -0.05+/-0.09mas in the ecliptic south. The ecliptic latitude dependence may also be represented by the linear relation, {Delta}{pi}~-0.22(+/-0.05)-0.003(+/-0.001)x{beta}mas ({beta} in degrees). Finally, there is a possible dependence of the parallax offset on distance, with the offset becoming negligible for {pi}<~1mas; we discuss whether this could be caused by a systematic error in the eclipsing binary distance scale, and reject this interpretation as unlikely.