We present the first direct search for exotic Higgs boson decays H -> AA, A -> gamma gamma 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 ffiffi experiment at V 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 -> 4 gamma) of (0.9-3.3) x 10-3 at 95% confidence level for masses of A in the range 0.1-1.2 GeV.