The first search for nonresonant production of Higgs boson pairs (HH) with one H decaying into four leptons and the other into a pair of b quarks is presented, using proton-proton collisions recorded at a center-of-mass energy of ss = 13 TeV by the CMS experiment. The analyzed data correspond to an integrated luminosity of 138 fb−1−1. A 95% confidence level upper limit of 32.4 is set on the signal strength modifier μ, defined as the ratio of the observed HH production rate in the HH→ZZ∗bb‾→4ℓbb‾HH→ZZ∗bb→4ℓbb decay channel to the standard model (SM) expectation. Possible modifications of the H trilinear coupling λHHHHHH with respect to the SM value are investigated. The coupling modifier κλλ, defined as λHHHHHH divided by its SM prediction, is constrained to be within the observed (expected) range −8.8 (−9.8) < κλλ< 13.4 (15.0) at 95% confidence level.[