We present the first direct search for exotic Higgs boson decays H→AA, A→γγ in events with two photonlike objects. The hypothetical particle A is a low-mass spin-0 particle decaying promptly to a merged diphoton reconstructed as a single photonlike object. We analyze the data collected by the CMS experiment at sqrt[s]=13 TeV corresponding to an integrated luminosity of 136 fb^{-1}. No excess above the estimated background is found. We set upper limits on the branching fraction B(H→AA→4γ) of (0.9-3.3)×10^{-3} at 95% confidence level for masses of A in the range 0.1-1.2 GeV.