  We present the results of a new, ultra-deep, near-infrared imaging survey
executed with the Hawk-I imager at the ESO VLT, of which we make all the data
public. This survey, named HUGS (Hawk-I UDS and GOODS Survey), provides deep,
high-quality imaging in the K and Y bands over the CANDELS UDS and GOODS-South
fields. We describe here the survey strategy, the data reduction process, and
the data quality. HUGS delivers the deepest and highest quality K-band images
ever collected over areas of cosmological interest, and ideally complements the
CANDELS data set in terms of image quality and depth. The seeing is exceptional
and homogeneous, confined to the range 0.38"-0.43". In the deepest region of
the GOODS-S field, (which includes most of the HUDF) the K-band exposure time
exceeds 80 hours of integration, yielding a 1-sigma magnitude limit of ~28.0
mag/sqarcsec. In the UDS field the survey matches the shallower depth of the
CANDELS images reaching a 1-sigma limit per sq.arcsec of ~27.3mag in the K band
and ~28.3mag in the Y-band, We show that the HUGS observations are well matched
to the depth of the CANDELS WFC3/IR data, since the majority of even the
faintest galaxies detected in the CANDELS H-band images are also detected in
HUGS. We present the K-band galaxy number counts produced by combining the HUGS
data from the two fields. We show that the slope of the number counts depends
sensitively on the assumed distribution of galaxy sizes, with potential impact
on the estimated extra-galactic background light (abridged).
