Abstract Protons consist of three valence quarks, two up-quarks and one down-quark, held together by gluons and a sea of quark-antiquark pairs. Collectively, quarks and gluons are referred to as partons. In a proton-proton collision, typically only one parton of each proton undergoes a hard scattering – referred to as single-parton scattering – leaving the remainder of each proton only slightly disturbed. Here, we report the study of double- and triple-parton scatterings through the simultaneous production of three J/ ψ mesons, which consist of a charm quark-antiquark pair, in proton-proton collisions recorded with the CMS experiment at the Large Hadron Collider. We observed this process – reconstructed through the decays of J/ ψ mesons into pairs of oppositely charged muons – with a statistical significance above five standard deviations. We measured the inclusive fiducial cross-section to be $$27{2}_{-104}^{+141}\,{{{\rm{(stat)}}}}\,\pm 17\,{{{\rm{(syst)}}}}\,{{{\rm{fb}}}}\,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>27</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>104</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>141</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace/> <mml:mi>(stat)</mml:mi> <mml:mspace/> <mml:mo>±</mml:mo> <mml:mn>17</mml:mn> <mml:mspace/> <mml:mi>(syst)</mml:mi> <mml:mspace/> <mml:mi>fb</mml:mi> </mml:mrow> </mml:math> , and compared it to theoretical expectations for triple-J/ ψ meson production in single-, double- and triple-parton scattering scenarios. Assuming factorization of multiple hard-scattering probabilities in terms of single-parton scattering cross-sections, double- and triple-parton scattering are the dominant contributions for the measured process.