  A realistic microscopic calculation of the unpolarized quark Generalized
Parton Distribution (GPD) $H_q^3$ of the $^3He$ nucleus is presented. In
Impulse Approximation, $H_q^3$ is obtained as a convolution between the GPD of
the internal nucleon and the non-diagonal spectral function, describing
properly Fermi motion and binding effects. The proposed scheme is valid at low
values of $\Delta^2$, the momentum transfer to the target, the most relevant
kinematical region for the coherent channel of hard exclusive processes. The
obtained formula has the correct forward limit, corresponding to the standard
deep inelastic nuclear parton distributions, and first moment, giving the
charge form factor of $^3He$. Nuclear effects, evaluated by a modern realistic
potential, are found to be larger than in the forward case. In particular, they
increase with increasing the momentum transfer when the asymmetry of the
process is kept fixed, and they increase with the asymmetry at fixed momentum
transfer. Another relevant feature of the obtained results is that the nuclear
GPD cannot be factorized into a $\Delta^2$-dependent and a
$\Delta^2$-independent term, as suggested in prescriptions proposed for finite
nuclei. The size of nuclear effects reaches 8 % even in the most important part
of the kinematical range under scrutiny. The relevance of the obtained results
to study the feasibility of experiments is addressed.
