The adoption of the International Celestial Reference System ICRS, and of the corresponding Frame, ICRF, by the 23rd General Assembly of the International Astronomical Union, calls for a redefinition of the departure point on the true equator. Several possibilities have been suggested. This paper considers the use of the non-rotating origin (Guinot, 1979, In: McCarthy D.D., Pilkington J.D. (eds.) Time and the Earth's Rotation. D. Reidel Pub. Co, p. 7). The ``Celestial Ephemeris Origin'' (CEO) is defined here as the non-rotating origin on the equator of the Celestial Ephemeris Pole (CEP). Developments valid at the microarcsecond, based on the best model for precession, nutation and pole offset at J2000.0 with respect to the pole of ICRF, are provided for computing the CEP coordinates and the position of the CEO. It is shown that an operational definition of UT1 based on the CEO leads to values which are insensitive at the microarcsecond level to future improvements of this model.