  The time delays of gravitationally lensed quasars are generally believed to
be unique numbers whose measurement is limited only by the quality of the light
curves and the models for the contaminating contribution of gravitational
microlensing to the light curves. This belief is incorrect -- gravitational
microlensing also produces changes in the actual time delays on the ~day(s)
light-crossing time scale of the emission region. This is due to a combination
of the inclination of the disk relative to the line of sight and the
differential magnification of the temperature fluctuations producing the
variability. We demonstrate this both mathematically and with direct
calculations using microlensing magnification patterns. Measuring these delay
fluctuations can provide a physical scale for microlensing observations,
removing the need for priors on either the microlens masses or the component
velocities. That time delays in lensed quasars are themselves time variable
likely explains why repeated delay measurements of individual lensed quasars
appear to vary by more than their estimated uncertainties. This effect is also
an important new systematic problem for attempts to use time delays in lensed
quasars for cosmology or to detect substructures (satellites) in lens galaxies.
