We describe the design, data analysis, and basic results of the Giant
Metrewave Radio Telescope Cold-HI AT (GMRT-CAT 1) survey, a
510-hour upgraded GMRT HI 21 cm emission survey of galaxies at in
the DEEP2 survey fields. The GMRT-CAT 1 survey is aimed at characterising HI
in galaxies during and just after the epoch of peak star-formation activity in
the Universe, a key epoch in galaxy evolution. We obtained high-quality HI 21
cm spectra for 11,419 blue star-forming galaxies at , in seven
pointings on the DEEP2 subfields. We detect the stacked HI 21 cm emission
signal of the 11,419 star-forming galaxies, which have an average stellar mass
of , at statistical significance,
obtaining an average HI mass of . This is significantly higher than the average HI mass of in star-forming galaxies at
with an identical stellar-mass distribution. We stack the
rest-frame 1.4 GHz continuum emission of our 11,419 galaxies to infer an
average star-formation rate (SFR) of . Combining
our average HI mass and average SFR estimates yields an HI depletion timescale
of Gyr, for star-forming galaxies at ,
times lower than that of local galaxies. We thus find that, although
main-sequence galaxies at have a high HI mass, their short HI
depletion timescale is likely to cause quenching of their star-formation
activity in the absence of rapid gas accretion from the circumgalactic medium.