We present high angular resolution imaging of the quasar PSO J172.3556+18.7734 at $z=6.82$ with the Very Long Baseline Array (VLBA). This source currently holds the record of being the highest redshift radio-loud quasar. These observations reveal a dominant radio source with a flux density of $398.4 pm 61.4~mu$Jy at 1.53 GHz, a deconvolved size of $9.9 times 3.5$ mas ($52.5 times 18.6$ pc), and an intrinsic brightness temperature of ($4.7 pm 0.7) times 10^7$ K. A weak unresolved radio extension from the main source is also detected at $sim~3.1sigma$ level. The total flux density recovered with the VLBA at 1.53 GHz is consistent with that measured with the Very Large Array (VLA) at a similar frequency. The quasar is not detected at 4.67 GHz with the VLBA, suggesting a steep spectral index with a limit of $alpha^{1.53}_{4.67} < -$1.55. The quasar is also not detected with the VLBA at 7.67 GHz. The overall characteristics of the quasar suggest that it is a very young radio source similar to lower redshift Gigahertz Peaked Spectrum radio sources, with an estimated kinematic age of $sim~10^3$ years. The VLA observations of this quasar revealed a second radio source in the field $23rlap{.}{}1$ away. This radio source, which does not have an optical or IR counterpart, is not detected with the VLBA at any of the observed frequencies. Its non-detection at the lowest observed VLBA frequency suggests that it is resolved out, implying a size larger than ~$0rlap{.}{}17$. It is thus likely situated at lower redshift than the quasar.
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