  The outer Galaxy is an environment with metallicity lower than the Solar one.
Because of this, the formation and survival of molecules in star-forming
regions located in the inner and outer Galaxy is expected to be different. To
gain understanding on how chemistry changes throughout the Milky Way, it is
crucial to observe outer Galaxy star-forming regions to constrain models
adapted for lower metallicity environments. In this paper we present a new
observational project: chemical complexity in star-forming regions of the outer
Galaxy (CHEMOUT). The goal is to unveil the chemical composition in 35 dense
molecular clouds associated with star-forming regions of the outer Galaxy
through observations obtained with the IRAM 30m telescope. In this first paper,
we present the sample, and report the detection at 3~mm of simple organic
species HCO+, H13CO+, HCN, c-C3H2, HCO, C4H, and HCS+, of the complex
hydrocarbon CH3CCH, and of SiO, CCS and SO. From c-C3H2, we estimate new
kinematic heliocentric and Galactocentric distances based on an updated
rotation curve of the Galaxy. The detection of the molecular tracers does not
seem to have a clear dependence on the Galactocentric distance. We also analyse
the HCO+ line profiles. We find high velocity wings in ~71% of the targets, and
their occurrence does not depend on the Galactocentric distance. Our results,
confirmed by a statistical analysis, show that the presence of organic
molecules and tracers of protostellar activity is ubiquitous in the
low-metallicity environment of the outer Galaxy. Based on this, and on the
additional evidence that small, terrestrial planets are omnipresent in the
Galaxy, we support previous claims that the definition of Galactic Habitable
Zone should be rediscussed in view of the ubiquitous capacity of the
interstellar medium to form organic molecules.
