1ES 1927+654 is a nearby active galactic nucleus (AGN) which underwent a changing-look event in early 2018, developing prominent broad Balmer lines which were absent in previous observations. We have followed up this object in the X-rays with an ongoing campaign that started in May 2018, and that includes 265 NICER (for a total of 678ks) and 14 Swift/XRT (26ks) observations, as well as three simultaneous XMM-Newton/NuSTAR (158/169 ks) exposures. In the X-rays, 1ES 1927+654 shows a behaviour unlike any previously known AGN. The source is extremely variable both in spectral shape and flux, and does not show any correlation between X-ray and UV flux on timescales of hours or weeks/months. After the outburst the power-law component almost completely disappeared, and the source showed an extremely soft continuum dominated by a blackbody component. The temperature of the blackbody increases with the luminosity, going from $kTsim 80$eV (for a 0.3--2keV luminosity of $L_{0.3-2}sim 10^{41.5}rm,erg,s^{-1}$) to $sim 200$eV (for $L_{0.3-2}sim 10^{44}rm,erg,s^{-1}$). The spectra show evidence of ionized outflows, and of a prominent feature at $sim 1$keV, which can be reproduced by a broad emission line. The unique characteristics of 1ES 1927+654 in the X-ray band suggest that it belongs to a new type of changing-look AGN. Future X-ray surveys might detect several more objects with similar properties.