We present VLBI Space Observatory Programme ( VSOP ) observations of the gamma-ray blazar 3C 279 at 1.6 and 5 GHz made on 1998 January 9-10 with the HALCA satellite and ground arrays including the Very Long Baseline Array ( VLBA ) . The combination of the VSOP and VLBA-only images at these two frequencies maps the jet structure on scales from 1 to 100 mas . On small angular scales the structure is dominated by the quasar core and the bright secondary component ‘ C4 ’ located 3 milliarcseconds from the core ( at this epoch ) at a position angle of - 115 ^ { \circ } . On larger angular scales the structure is dominated by a jet extending to the southwest , which at the largest scale seen in these images connects with the smallest scale structure seen in VLA images . We have exploited two of the main strengths of VSOP : the ability to obtain matched-resolution images to ground-based images at higher frequencies and the ability to measure high brightness temperatures . A spectral index map was made by combining the VSOP 1.6 GHz image with a matched-resolution VLBA-only image at 5 GHz from our VSOP observation on the following day . The spectral index map shows the core to have a highly inverted spectrum , with some areas having a spectral index approaching the limiting value for synchrotron self-absorbed radiation of \alpha = +2.5 ( where S \propto \nu ^ { + \alpha } ) . Gaussian model fits to the VSOP visibilities revealed high brightness temperatures ( > 10 ^ { 12 } K ) that are difficult to measure with ground-only arrays . An extensive error analysis was performed on the brightness temperature measurements . Most components did not have measurable brightness temperature upper limits , but lower limits were measured as high as 5 ~ { } \times~ { } 10 ^ { 12 } K. This lower limit is significantly above both the nominal inverse Compton and equipartition brightness temperature limits . The derived Doppler factor , Lorentz factor , and angle to the line-of-sight in the case of the equipartition limit are at the upper end of the range of expected values for EGRET blazars .