Based on 368.5 pb−1 of e+e− collision data collected at center-of-mass energies 4.914 and 4.946 GeV by the BESIII detector, the e+e−→ϕχc1(3872) process is searched for the first time. No significant signal is observed and the upper limits at the 90% confidence level on the product of the Born cross section σ(e+e−→ϕχc1(3872)) and the branching fraction B[χc1(3872)→π+π−J/ψ] at 4.914 and 4.946 GeV are set to be 0.85 and 0.96 pb, respectively. These measurements provide useful information for the production of the χc1(3872) at e+e− colliders and deepen our understanding about the nature of this particle. Published by the American Physical Society 2024