The Astronomical Unit is obtained by measuring the Doppler shift relative to the Earth of the narrow spectral features of galactic neutral hydrogen at 21 cm. The features chosen were the narrow absorption components in the spectra of Cassiopeia A, Taurus A and the emission at 1 - 0 = 0.00. Observations which were taken over the period of one year gave two largely independent estimates of the Astronomical Unit which were combined to yield a value of 14963S000119000 (p.e.) km. This agrees with the value adopted by the IAU based on the radar value but it disagrees with the value determined optically by Rabe using a dynamical method.