  Most runaway OB stars, like the majority of massive stars residing in their
parent clusters, go through the red supergiant (RSG) phase during their
lifetimes. Nonetheless, although many dozens of massive runaways were found to
be associated with bow shocks, only two RSG bow-shock-producing stars,
Betelgeuse and \mu Cep, are known to date. In this paper, we report the
discovery of an arc-like nebula around the late M-type star IRC-10414 using the
SuperCOSMOS H-alpha Survey. Our spectroscopic follow-up of IRC-10414 with the
Southern African Large Telescope (SALT) showed that it is a M7 supergiant,
which supports previous claims on the RSG nature of this star based on
observations of its maser emission. This was reinforced by our new radio- and
(sub)millimeter-wavelength molecular line observations made with the Atacama
Pathfinder Experiment (APEX) 12 meter telescope and the Effelsberg 100 m radio
telescope, respectively. The SALT spectrum of the nebula indicates that its
emission is the result of shock excitation. This finding along with the
arc-like shape of the nebula and an estimate of the space velocity of IRC-10414
(\approx 70\pm20 km/s) imply the bow shock interpretation for the nebula. Thus,
IRC-10414 represents the third case of a bow-shock-producing RSG and the first
one with a bow shock visible at optical wavelengths. We discuss the smooth
appearance of the bow shocks around IRC-10414 and Betelgeuse and propose that
one of the necessary conditions for stability of bow shocks generated by RSGs
is the ionization of the stellar wind. Possible ionisation sources of the wind
of IRC-10414 are proposed and discussed.
