We analyze data returned by the Magnetospheric Multiscale mission (MMS) constellation during a rapid (∼1.5 s) traversal of a flapping and reconnecting current sheet (CS) in the near‐Earth magnetotail (X ∼−20 RE). The CS was highly tilted, with its normal pointing strongly duskward. Its extreme thinness was confirmed by a curvature analysis of the magnetic field lines. The event was associated with a guide field of 8% of the reconnecting components. From the pitch angle distributions of low‐energy electrons we infer a crossing earthward of the X‐line. Traveling practically normal to the CS, MMS encountered an ion diffusion region (IDR) in which was embedded an electron diffusion region (EDR). IDR signatures included breaking of the ion frozen‐in condition in the presence of Hall B and E fields. EDR signatures included a strong out‐of‐plane current associated with a superAlfvénic electron jet, positive energy transfer, and a temperature anisotropy (Te∥ > Te⊥) which disappeared at the field reversal. Derived scale sizes normal to the CS are: ∼6.9 de (EDR) and ∼0.4 di (IDR; 40 and 100 km). We estimate the average dimensionless reconnection rate as 0.077 ± 0.050. The observations and inferences are supported by particle‐in‐cell (PIC) numerical simulations. We find very good agreement in the reconnection rates. We also discuss the effects of asymmetries in the density, temperature and magnetic field strength on the Hall fields and length of the outflow jets. The event is associated with a substorm onset which began 7 min after the MMS observations.