We describe the design, data analysis, and basic results of the Giant Metrewave Radio Telescope Cold-HI AT z ≈ 1 (GMRT-CATz1) survey, a 510-hour upgraded GMRT HI 21 cm emission survey of galaxies at z = 0.74 − 1.45 in the DEEP2 survey fields. The GMRT-CATz1 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 z = 0.74 − 1.45, 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 M * ≈ 10 10 M , at 7.1σ statistical significance, obtaining an average HI mass of M HI = (13.7 ± 1.9) × 10 9 M . This is significantly higher than the average HI mass of M HI = (3.96 ± 0.17) × 10 9 M in star-forming galaxies at z ≈ 0 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 8.07 ± 0.82 M yr −1 . Combining our average HI mass and average SFR estimates yields an HI depletion timescale of 1.70 ± 0.29 Gyr, for star-forming galaxies at z ≈ 1, ≈ 3 times lower than that of local galaxies. We thus find that, although main-sequence galaxies at z ≈ 1 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.