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In the field of astrophysics, the faint signal from distant galaxies and other dim cosmological sources at millimeter and submillimeter wavelengths require the use of high-sensitivity experiments. Cryogenics and the use of low-temperature detectors are essential to the accomplishment of the scientific objectives, allowing lower detector noise levels and improved instrument stability. Bolometric detectors are usually cooled to temperatures below 1K, and the constraints on the instrument are stringent, whether the experiment is a space-based platform or a ground-based telescope. The latter are usually deployed in remote and harsh environments such as the South Pole, where maintenance needs to be kept minimal. CEA-SBT has acquired a strong heritage in the development of vibration-free multistage helium-sorption coolers, which can provide cooling down to 200 mK when mounted on a cold stage at temperatures <5K. In this paper, we focus on the development of a three-stage cooler dedicated to the BICEP Array project led by Caltech/JPL, which aims to study the birth of the Universe and specifically the unique B-mode pattern imprinted by primordial gravitational waves on the polarization of the Cosmic Microwave Background. Several cryogenic receivers are being developed, each featuring one such helium-sorption cooler operated from a 4K stage cooled by a Cryomech pulse-tube with heat lifts of >1.35W at 4.2K and >36W at 45K. The major challenge of this project is the large masses to be cooled to sub-kelvin temperatures (26 kg at 250mK) and the resulting long cool-down time, which in this novel cooler design is kept to a minimum with the implementation of passive and active thermal links between different temperature stages. A first unit has been sized to provide 230, 70 and 2μW of net heat lifts at the maximum temperatures of 2.8K, 340 and 250mK, respectively, for a minimum duration of 48 hours.