A Dalitz plot analysis of B0→ηc(1S)K+π- decays is performed using data samples of pp collisions collected with the LHCb detector at centre-of-mass energies of s=7,8 and 13TeV , corresponding to a total integrated luminosity of 4.7fb-1 . A satisfactory description of the data is obtained when including a contribution representing an exotic ηc(1S)π- resonant state. The significance of this exotic resonance is more than three standard deviations, while its mass and width are 4096±20-22+18MeV and 152±58-35+60MeV , respectively. The spin-parity assignments JP=0+ and JP=1- are both consistent with the data. In addition, the first measurement of the B0→ηc(1S)K+π- branching fraction is performed and gives B(B0→ηc(1S)K+π-)=(5.73±0.24±0.13±0.66)×10-4, where the first uncertainty is statistical, the second systematic, and the third is due to limited knowledge of external branching fractions.