  We outline a mission with the aim of directly detecting the gravitomagnetic
field of the Earth. This mission is called Gravity Probe C. Gravity Probe
C(lock) is based on a recently discovered and surprisingly large
gravitomagnetic clock effect. The main idea is to compare the proper time of
two standard clocks in direct and retrograde orbits around the Earth. After one
orbit the proper time difference of two such clocks is predicted to be of the
order of $2\times 10^{-7}$ s. The conceptual difficulty to perform Gravity
Probe C is expected to be comparable to that of the Gravity Probe B--mission.
