  Long-duration gamma-ray bursts (GRBs) are powerful tracers of star-forming
galaxies. We have defined a homogeneous subsample of 69 Swift GRB-selected
galaxies spanning a very wide redshift range. Special attention has been
devoted to making the sample optically unbiased through simple and well-defined
selection criteria based on the high-energy properties of the bursts and their
positions on the sky. Thanks to our extensive follow-up observations, this
sample has now achieved a comparatively high degree of redshift completeness,
and thus provides a legacy sample, useful for statistical studies of GRBs and
their host galaxies. In this paper we present the survey design and summarize
the results of our observing program conducted at the ESO Very Large Telescope
(VLT) aimed at obtaining the most basic properties of galaxies in this sample,
including a catalog of R and Ks magnitudes and redshifts. We detect the host
galaxies for 80 % of the GRBs in the sample, although only 42 % have Ks-band
detections, which confirms that GRB-selected host galaxies are generally blue.
The sample is not uniformly blue, however, with two extremely red objects
detected. Moreover, galaxies hosting GRBs with no optical/NIR afterglows, whose
identification therefore relies on X-ray localizations, are significantly
brighter and redder than those with an optical/NIR afterglow. Our spectroscopic
campaign has resulted in 77 % now having redshift measurements, with a median
redshift of 2.14 +- 0.18. TOUGH alone includes 17 detected z > 2 Swift GRB host
galaxies suitable for individual and statistical studies. Seven hosts have
detections of the Ly-alpha emission line and we can exclude an early indication
that Ly-alpha emission is ubiquitous among GRB hosts, but confirm that Ly-alpha
is stronger in GRB-selected galaxies than in flux-limited samples of Lyman
break galaxies.
