The first observation of the Bs0​→ (χc1(3872) → J/ψπ+π−)π+π− decay is reported using proton-proton collision data, corresponding to integrated luminosities of 1, 2 and 6 fb−1, collected by the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, respectively. The ratio of branching fractions relative to the Bs0​→ (ψ(2S) → J/ψπ+π−)π+π− decay is measured to be B(Bs0→χc1(3872)π+π−)×B(χc1(3872)→J/ψπ+π−)B(Bs0→ψ(2S)π+π−)×B(ψ(2S)→J/ψπ+π−)=(6.8±1.1±0.2)×10−2,B(Bs0​→ψ(2S)π+π−)×B(ψ(2S)→J/ψπ+π−)B(Bs0​→χc1​(3872)π+π−)×B(χc1​(3872)→J/ψπ+π−)​=(6.8±1.1±0.2)×10−2,where the first uncertainty is statistical and the second systematic. The mass spectrum of the π++π− system recoiling against the χc1c1​(3872) meson exhibits a large contribution from Bs0​→ χc1​(3872) (f0​(980) → π+π−) decays. [graphic not available: see full fulltext]