Very-long-baseline interferometry images of the nuclear region of the radio galaxy Cygnus A reveal a pronounced "core" and a knotty jet and counterjet. The knots are moving away from the core at apparent speeds which are subluminal for h = 1 [h = H0/100 km.s-1.Mpc-1;1 parsec (pc) = 3.09 x 10(16)m] and about c for h = 0.5. The jet is aligned with the outer, kiloparsec-scale jet to within 2 degrees. The counterjet has a total flux density at 5 GHz of about one-fifth of that of the jet. In the context of the twin relativistic jet model for active galactic nuclei, the jet in Cygnus A is oriented at an angle to our line of sight of 35-80 degrees and 55-85 degrees, and the intrinsic velocity of the jet fluid is 0.4-0.6c and 0.6-1c for h = 1 and h = 0.5, respectively.