We have measured the noise temperature of a single, sensitive superconducting NbN hot electron bolometer (HEB) mixer in a frequency range from 1.6 to 5.3 THz, using a setup with all the key components in vacuum. By analyzing the measured receiver noise temperature using a quantum noise (QN) model for HEB mixers, we confirm the effect of QN. The QN is found to be responsible for about half of the receiver noise at the highest frequency in our measurements. The β -factor (the quantum efficiency of the HEB) obtained experimentally agrees reasonably well with the calculated value. We acknowledge S.C. Shi for supporting this joint research project. The work was supported by China Exchange Programme executed by KNAW and CAS, the NSFC under Grant Nos. 10803021 and 10621303, the AMSTAR+ of RadioNet under FP7, and NWO.