  We present a method for measuring electrical currents enclosed by flux rope
structures that are ejected within solar coronal mass ejections (CMEs). Such
currents are responsible for providing the Lorentz self-force that propels
CMEs. Our estimates for the driving current are based on measurements of the
propelling force obtained using data from the LASCO coronagraphs aboard the
SOHO satellite. We find that upper limits on the currents enclosed by CMEs are
typically around $10^{10}$ Amperes. We estimate that the magnetic flux enclosed
by the CMEs in the LASCO field of view is a few $\times 10^{21}$ Mx.
