We present sensitive, multifrequency Very Long Baseline Array (VLBA) images of the nuclear radio sources of NGC 1068. At 5 GHz and 8.4 GHz, the radio continuum source S1, argued to mark the location of the hidden active nucleus, resolves into an elongated, ~ 0.8 pc source oriented nearly at right angles to the radio jet axis but more closely aligned to the distribution of the nuclear H2O maser spots. S1 is detected at 5 GHz but not at 1.4 GHz, indicating strong free-free absorption below 5 GHz,

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... and it has a flat spectrum between 5 GHz and 8.4 GHz. A 5/8.4 GHz spectral index map reveals an unresolved, inverted spectrum source at the center of the S1 structure which may mark the AGN proper. The average brightness temperature is too low for synchrotron self-absorption to impact the integrated spectrum significantly. In addition, a careful registration with the nuclear H2O masers argues that the S1 continuum source arises from the inner regions of the maser disk rather than a radio jet. The emission mechanism may be direct, thermal free-free emission from an X-ray-heated corona or wind arising from the molecular disk. We demonstrate that the hidden active nucleus is sufficiently luminous, to within the current estimates, to provide the requisite heating.