  We present a pilot, untargeted extragalactic carbon monoxide (CO)
emission-line survey using ALMACAL, a project utilizing ALMA calibration data
for scientific purposes. In 33 deep (Texp > 40 min) ALMACAL fields we report
six CO emission-line detections above S/N > 4, one-third confirmed by MUSE
observations. With this pilot survey, we probe a cosmologically significant
volume of ~10^5 cMpc^3, widely distributed over many pointings in the southern
sky, making the survey largely insusceptible to the effects of cosmic variance.
We derive the redshift probability of the CO detections using probability
functions from the Shark semi-analytical model of galaxy formation. By assuming
typical CO excitations for the detections, we put constraints on the cosmic
molecular gas mass density evolution over the redshift range 0 < z < 1.5. The
results of our pilot survey are consistent with the findings of other
untargeted emission-line surveys and the theoretical model predictions and
currently cannot rule out a non-evolving molecular gas mass density. Our study
demonstrates the potential of using ALMA calibrator fields as a multi-sightline
untargeted CO emission line survey. Applying this approach to the full ALMACAL
database will provide an accurate, free of cosmic variance, measurement of the
molecular luminosity function as a function of redshift.
