We present a detailed study of a peculiar source detected in the COSMOS survey at z = 0.359. Source CXOC J100043.1+020637, also known as CID-42, has two compact optical sources embedded in the same galaxy. The distance between the two, measured in the HST/ACS image, is 0.495" ± 0.005" that, at the redshift of the source, corresponds to a projected separation of 2.46 ± 0.02 kpc. A large (~1200 km s-1) velocity offset between the narrow and broad components of Hβ has been measured in three different optical spectra from the VLT/VIMOS and Magellan/IMACS instruments. CID-42 is also the only X-ray source in COSMOS, having in its X-ray spectra a strong redshifted broad absorption iron line and an iron emission line, drawing an inverted P-Cygni profile. The Chandra and XMM-Newton data show that the absorption line is variable in energy by ΔE = 500 eV over four years and that the absorber has to be highly ionized in order not to leave a signature in the soft X-ray spectrum. That these features—the morphology, the velocity offset, and the inverted P-Cygni profile—occur in the same source is unlikely to be a coincidence. We envisage two possible explanations, both exceptional, for this system: (1) a gravitational wave (GW) recoiling black hole (BH), caught 1-10 Myr after merging; or (2) a Type 1/Type 2 system in the same galaxy where the Type 1 is recoiling due to the slingshot effect produced by a triple BH system. The first possibility gives us a candidate GW recoiling BH with both spectroscopic and imaging signatures. In the second case, the X-ray absorption line can be explained as a BAL-like outflow from the foreground nucleus (a Type 2 AGN) at the rearer one (a Type 1 AGN), which illuminates the otherwise undetectable wind, giving us the first opportunity to show that fast winds are present in obscured active galactic nuclei (AGNs), and possibly universal in AGNs.