  In turbulent flows the $n$'th order structure functions $S_n(R)$ scale like
$R^{\zeta_n}$ when $R$ is in the "inertial range". Extended Self-Similarity
refers to the substantial increase in the range of power law behaviour of
$S_n(R)$ when they are plotted as a function of $S_2(R)$ or $S_3(R)$. In this
Letter we demonstrate this phenomenon analytically in the context of the
``multiscaling" turbulent advection of a passive scalar. This model gives rise
to a series of differential equations for the structure functions $S_n(R)$
which can be solved and shown to exhibit extended self similarity. The
phenomenon is understood by comparing the equations for $S_n(R)$ to those for
$S_n(S_2)$.
