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We investigate the nature and classification of PMNJ1603-4904, a bright radio source close to the Galactic plane, which is associated with one of the brightest hard-spectrum gamma-ray sources detected by Fermi/LAT. It has previously been classified as a low-peaked BL Lac object based on its broadband emission and the absence of optical emission lines. Optical measurements, however, suffer strongly from extinction and the absence of pronounced short-time gamma-ray variability over years of monitoring is unusual for a blazar. We are combining new and archival multiwavelength data in order to reconsider the classification and nature of this unusual gamma-ray source. For the first time, we study the radio morphology at 8.4GHz and 22.3GHz, and its spectral properties on milliarcsecond (mas) scales, based on VLBI observations from the TANAMI program. We combine the resulting images with multiwavelength data in the radio, IR, optical/UV, X-ray, and gamma-ray regimes. PMNJ1603-4904 shows a symmetric brightness distribution at 8.4GHz on mas-scales, with the brightest, and most compact component in the center of the emission region. The morphology is reminiscent of a Compact Symmetric Object (CSO). Such objects have been predicted to produce gamma-ray emission but have not been detected as a class by Fermi/LAT so far. Sparse (u, v)-coverage at 22.3GHz prevents an unambiguous modeling of the source morphology. IR measurements reveal an excess in the spectral energy distribution (SED), which can be modeled with a blackbody with a temperature of about 1600K, and which is usually not present in blazar SEDs. The VLBI data and the shape of the SED challenge the current blazar classification. PMNJ1603-4904 seems to be either a highly peculiar BL Lac object or a misaligned jet source. In the latter case, the intriguing VLBI structure opens room for a possible classification as a gamma-ray bright CSO.