According to recent results of Ho & Heinke, the Cassiopeia A supernova remnant contains a young (≈330-yr-old) neutron star (NS) which has carbon atmosphere and shows notable decline of the effective surface temperature. We report a new (2010 November) Chandra observation which confirms the previously reported decline rate. The decline is naturally explained if neutrons have recently become superfluid (in triplet state) in the NS core, producing a splash of neutrino emission due to Cooper pair formation (CPF) process that currently accelerates the cooling. This scenario puts stringent constraints on poorly known properties of NS cores: on density dependence of the temperature Tcn(ρ) for the onset of neutron superfluidity [Tcn(ρ) should have a wide peak with maximum ≈ (7–9) × 108 K]; on the reduction factor q of CPF process by collective effects in superfluid matter (q > 0.4) and on the intensity of neutrino emission before the onset of neutron superfluidity (30–100 times weaker than the standard modified Urca process). This is serious evidence for nucleon superfluidity in NS cores that comes from observations of cooling NSs.