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We present a novel scenario for the growth of dust grains in galaxies athigh-redshift ($z\sim 6$). In our model, the mechanical feedback from massivestar clusters evolving within high-density pre-enriched media allows to pile-upa large amount of matter into massive supershells. If the gas metallicity($\geq$ Z$_{\odot}$), number density ($\geq 10^6$ cm$^{-3}$) and dust-to-gasmass ratio ($\sim 1/150 \times Z$) within the supershell are sufficientlylarge, such supershells may become optically thick to the starlight emergingfrom their host star clusters and even to radiation from the Cosmic MicrowaveBackground (CMB). Based on semi-analytic models, we argue that this mechanism,occurring in the case of massive ($\geq 10^7$ M$_{\odot}$) molecular cloudshosting $\geq 10^6$ M$_{\odot}$ star clusters, allows a large mass of gas anddust to acquire a temperature below that of the CMB, whereupon dust graingrowth may occur with ease. In galaxies with total stellar mass $M_{*}$, graingrowth within supershells may increase the dust mass by $\sim 10^6$ M$_{\odot}$$(M_{*}/10^{8}$ M$_{\odot}$).

Dust Grain Growth at High Redshift: Starburst-driven CMB-Dark Supershells