We report on the quiescent X‐ray properties of the recently discovered transiently accreting 11‐Hz X‐ray pulsar in the globular cluster Terzan 5. Using two archival Chandra observations, we demonstrate that the quiescent spectrum of this neutron star low‐mass X‐ray binary is soft and can be fit to a neutron star atmosphere model with a temperature of kT∞∼ 73 eV. A power‐law spectral component is not required by the data and contributes at most ∼20 per cent to the total unabsorbed 0.5–10 keV flux of ∼9 × 10−14 erg cm−2 s−1. Such a soft quiescent spectrum is unusual for neutron stars with relatively high inferred magnetic fields and casts a different light on the interpretation of the hard spectral component, which is often attributed to magnetic field effects. For a distance of 5.5 kpc, the estimated quiescent thermal bolometric luminosity is ∼6 × 1032 erg s−1. If the thermal emission is interpreted as cooling of the neutron star, the observed luminosity requires that the system is quiescent for at least ∼100 yr. Alternatively, enhanced neutrino emissions can cool the neutron star to the observed quiescent luminosity.