A major radio outburst in III Zw 2 with an extremely inverted, millimeter-peaked spectrum

III Zw 2 is a spiral galaxy with an optical spectrum and faint extended radio structure typical of a Seyfert galaxy, but also with an extremely variable, blazar-like radio core. We have now discovered a new radio flare in which the source has brightened more than 20-fold within less than 2 yr. A broadband radio spectrum between 1.4 and 666 GHz shows a textbook-like synchrotron spectrum peaking at 43 GHz, with a self-absorbed synchrotron spectral index +2.5 at frequencies below 43 GHz and an optically thin spectral index -0.75 at frequencies above 43 GHz. The outburst spectrum can be well fitted by two homogenous, spherical components with equipartition sizes of 0.1 and 0.2 pc at 43 and 15 GHz and with magnetic fields of 0.4 and 1 G. VLBA observations at 43 GHz confirm this double structure and these sizes. Timescale arguments suggest that the emitting regions are shocks which are continuously accelerating particles. This could be explained by a frustrated jet scenario with very compact hot spots. Similar millimeter-peaked spectrum sources could have escaped our attention because of their low flux density at typical survey frequencies and their strong variability.