NGC 2770 has been the host of three supernovae (SNe) of Type Ib during the last ten years, SN 1999eh, SN 2007uy, and SN 2008D. SN 2008D attracted special attention due to the serendipitous discovery of an associated X-ray transient. In this paper, we study the properties of NGC 2770 and specifically the three SN sites to investigate whether this galaxy is in any way peculiar to cause a high frequency of SNe Ib. We model the global spectral energy distribution of the galaxy from broadband data and derive a star formation and SN rate comparable to the values of the Milky Way. We further study the galaxy using longslit spectroscopy covering the major axis and the three SN sites. From the spectroscopic study we find subsolar metallicities for the SN sites, a high extinction and a moderate star formation rate. In a high-resolution spectrum, we also detect diffuse interstellar bands in the line of sight toward SN 2008D. A comparison of NGC 2770 to the global properties of a galaxy sample with high SN occurrence (>= 3 SN in the last 100 years) suggests that NGC 2770 is not particularly destined to produce such an enhancement of observed SNe. Its properties are also very different from gamma-ray burst host galaxies. Statistical considerations on SN Ib detection rates give a probability of similar to 1.5% to find a galaxy with three Ib SNe detected in ten years. The high number of rare Ib SNe in this galaxy is therefore likely to be a coincidence rather than special properties of the galaxy itself. NGC 2770 has a small irregular companion, NGC 2770B, which is highly star-forming, has a very low mass and one of the lowest metallicities detected in the nearby universe as derived from longslit spectroscopy. In the most metal poor part, we even detect Wolf-Rayet (WR) features, which is at odds with most current models of WR stars which require high metallicities.