We observed the nuclear region of NGC 4261 (3C 270) with VLBI to determine the morphology of the central radio source on parsec scales and in particular to see whether the inner radio axis remained in the same direction as the kiloparsec-scale jets or whether it was aligned with the apparent rotation axis of the nuclear disk imaged by HST. The position angle of the radio axis in our Very Long Baseline Array (VLBA) images agrees, within the errors, with the position angle of the VLA-scale jet. Thus, there is no evidence for precession of the jets on timescales shorter than the material propagation time from the nucleus to the diffuse radio lobes. Our dual frequency observations also reveal basically symmetric radio structures at both 1.6 and 8.4 GHz. Analysis of these images shows that most of the central 10 pc of this source is not significantly affected by free-free absorption, even though HST images of the nucleus of the galaxy show it to contain a nearly edge-on disk of gas and dust on larger scales. The lack of detectable absorption over most of the central 10 pc implies that the density of ionized gas in this region is less than ~103 cm-3, assuming a temperature of ~104 K. Our highest angular resolution images show a very narrow absorption feature just east of the radio core, suggesting that there may be a small, dense inner accretion disk with a width of less than 0.1 pc. If the inclination of this inner disk is close to that of the larger scale HST disk, it becomes optically thin to 8.4 GHz radiation at a deprojected radius of about 0.8 pc. The brightness of the parsec-scale jets falls off very rapidly on both sides of the core, suggesting that the jets are rapidly expanding during the first several parsecs of their travel. The rate of jet expansion must slow when the internal pressure falls below that of the external medium. We suggest that this occurs between about 10 and 200 pc from the core because the rate of decrease in radio brightness is far slower at more than 200 pc from the core than it is within 10 pc of the core. It appears that there is a small, dense inner disk centered on the radio core (the base of the jets; less than 1 pc), a low-density, presumably hot "bubble" filling most of the inner several parsecs of the nucleus (within which the radio jets expand rapidly; ~10 pc), and a surrounding cool, higher density region (of which the HST absorption disk is part; >10 pc) within which the transverse expansion of the radio jets, as implied by the rate of decrease in jet brightness, is nearly halted.