The first observation of the concurrent production of two 𝐽/𝜓 mesons in proton-nucleus collisions is presented. The analysis is based on a proton-lead (𝑝⁢Pb) data sample recorded at a nucleon-nucleon center-of-mass energy of 8.16 TeV by the CMS experiment at the CERN LHC and corresponding to an integrated luminosity of 174.6  nb−1. The two 𝐽/𝜓 mesons are reconstructed in their 𝜇+⁢𝜇− decay channels with transverse momenta 𝑝T >6.5  GeV and rapidity |𝑦| <2.4. Events where one of the 𝐽/𝜓 mesons is reconstructed in the dielectron channel are also considered in the search. The 𝑝⁢Pb →𝐽/𝜓⁢𝐽/𝜓+𝑋 process is observed with a significance of 5.3 standard deviations. The measured inclusive fiducial cross section, using the four-muon channel alone, is 𝜎⁡(𝑝⁢Pb →𝐽/𝜓⁢𝐽/𝜓 +𝑋) = 22.0 ±8.9⁢(stat) ±1.5⁢(syst)  nb. A fit of the data to the expected rapidity separation for pairs of 𝐽/𝜓 mesons produced in single (SPS) and double (DPS) parton scatterings yields 𝜎𝑝⁢Pb→𝐽/𝜓⁢𝐽/𝜓+𝑋
SPS=16.5±10.8⁢(stat)±0.1⁢(syst)  nb and 𝜎𝑝⁢Pb→𝐽/𝜓⁢𝐽/𝜓+𝑋
DPS =5.4 ±6.2⁢(stat) ±0.4⁢(syst)  nb, respectively. This latter result can be transformed into a lower bound on the effective DPS cross section, closely related to the squared average interparton transverse separation in the collision, of 𝜎eff >1.0  mb at 95% confidence level.