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We have exploited ALMA calibration observations to carry out a novel, wideand deep submm survey, ALMACAL. These calibration data comprise a large numberof observations of calibrator fields in a variety of frequency bands and arrayconfigurations. Gathering together data acquired during multiple visits to manyALMA calibrators, it is possible to reach noise levels which allow thedetection of faint dusty, star-forming galaxies (DSFGs) over a significantarea. In this paper we outline our survey strategy and report the firstresults. We have analysed data for 69 calibrators, reaching depths of $\sim 25\, {\rm \mu Jy \, beam^{-1}}$ at sub-arcsec resolution. Adopting a conservativeapproach based on $\geq 5 \sigma$ detections, we have found eight and 11 DSFGsin ALMA bands 6 and 7, respectively, with flux densities $S_{\rm 1.2 mm} \geq0.2 \, {\rm mJy}$. The faintest galaxies would have been missed by even thedeepest \emph{Herschel} surveys. Our cumulative number counts have beendetermined independently at 870 $\mu$m and 1.2 mm, from a sparse sampling ofthe astronomical sky, and are thus relatively free of cosmic variance. Thecounts are lower than reported previously by a factor of at least $2\times$.Future analyses will yield large, secure samples of DSFGs, with redshiftsdetermined via detection of submm spectral lines. Uniquely, our strategy thenallows morphological studies of very faint DSFGs - representative of morenormal star-forming galaxies than conventional submm galaxies (SMGs) - infields where self-calibration is feasible, yielding milliarcsecond spatialresolution.

ALMACAL I: First dual-band number counts from a deep and wide ALMA submm survey, free from cosmic variance