  A microscopic calculation of the effective mass of one $^4$He impurity in
homogeneous liquid $^3$He at zero temperature is performed for an extended
Jastrow--Slater wave function, including two-- and three--body dynamical
correlations and also backflow correlations between the $^4$He atom and the
particles in the medium. The effective mass at saturation density,
$m_4^*/m_4=1.21$, is in very good agreement with the recent experimental
determination by Edwards {\it et al}. The three-- particle correlations appear
to give a small contribution to the effective mass and different approximations
for the three--particle distribution function give almost identical results for
$m_4^*/m_4$.
