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 carr
iers 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.
