The detection of habitable worlds is one of humanity’s greatest endeavors. Thus far, astrobiological studies have shown that one of the most critical components for allowing life to develop is liquid water. Its chemical properties and its capacity to dissolve and, hence, transport other substances makes this constituent a key piece in this regard. As a consequence, looking for life as we know it is directly related to the search for liquid water. For a remote detection of life in distant planetary systems, this essentially means looking for planets in the so-called habitable zone. In this sense, K-dwarf stars are the perfect hosts to search for planets in this range of distances. Contrary to G-dwarfs, the habitable zone is closer, thus making planet detection easier using transit or radial velocity techniques. Contrary to M-dwarfs, stellar activity is on a much smaller scale, hence, it has a smaller impact in terms of both the detectability and the true habitability of the planet. Also, K-dwarfs are the quietest in terms of oscillations, and granulation noise. In spite of this, there is a dearth of planets in the habitable zone of K-dwarfs due to a lack of observing programs devoted to this parameter space. In response to a call for legacy programs of the Calar Alto observatory, we have initiated the first dedicated and systematic search for habitable planets around these stars: K-dwarfs Orbited By habitable Exoplanets (KOBE). This survey is monitoring the radial velocity of 50 carefully pre-selected K-dwarfs with the CARMENES instrument over five semesters, with an average of 90 data points per target. Based on planet occurrence rates convolved with our detectability limits, we expect to find 1.68 ± 0.25 planets per star in the KOBE sample. Furthermore, in half of the sample, we expect to find one of those planets within the habitable zone. Here, we describe the motivations, goals, and target selection for the project as well as the preliminary stellar characterization.