We present the discovery and high-cadence follow-up observations of SN2018ivc, an unusual SNeII that exploded in NGC1068 (D=10.1Mpc). The light curve of SN2018ivc declines piecewise-linearly, changing slope frequently, with four clear slope changes in the first 30days of evolution. This rapidly changing light curve indicates that interaction between the circumstellar material and ejecta plays a significant role in the evolution. Circumstellar interaction is further supported by a strong X-ray detection. The spectra are rapidly evolving and dominated by hydrogen, helium, and calcium emission lines. We identify a rare high-velocity emission-line feature blueshifted at ~7800km/s (in H{alpha}, H{beta}, P{beta}, P{gamma}, HeI, and CaII), which is visible from day 18 until at least day 78 and could be evidence of an asymmetric progenitor or explosion. From the overall similarity between SN2018ivc and SN1996al, the H{alpha} equivalent width of its parent HII region, and constraints from pre-explosion archival Hubble Space Telescope images, we find that the progenitor of SN2018ivc could be as massive as 52 M{odot} but is more likely <12M{odot}. SN2018ivc demonstrates the importance of the early discovery and rapid follow-up observations of nearby supernovae to study the physics and progenitors of these cosmic explosions.