  We have synthesized highly oxygen deficient HfO$_{2-x}$ thin films by
controlled oxygen engineering using reactive molecular beam epitaxy. Above a
threshold value of oxygen vacancies, p-type conductivity sets in with up to 6
times 10^{21} charge carriers per cm3. At the same time, the band-gap is
reduced continuously by more than 1 eV. We suggest an oxygen vacancy induced
p-type defect band as origin of the observed behavior.
