Using a sample of (10.09±0.04)×10 9 J/ψ events collected with the BESIII detector operating at the BEPCII storage ring, a partial wave analysis of the decay J/ψ → γηη ′ is performed. The first observation of an isoscalar state with exotic quantum numbers J P C = 1 −+ , denoted as η1(1855), is reported in the process J/ψ → γη1(1855) with η1(1855) → ηη ′ . Its mass and width are measured to be (1855±9 +6−1 ) MeV/c 2 and (188±18 +3 −8 ) MeV, respectively, where the first uncertainties are statistical and the second are systematic, and its statistical significance is estimated to be larger than 19σ.