  It is shown that neutrino mixing angles which are consistent with current
experimental observations may be naturally obtained in a Pati-Salam model
constructed from intersecting D6 branes on a $T^6/(Z_2 \times Z_2)$
orientifold. The Dirac mass matrices in the model are naturally the same as
those which are obtained by imposing a $\mathbf{\Delta(27)}$ flavor symmetry,
which allows for near-tribimaximal mixing in the neutrino sector. In addition,
it is possible to obtain the correct mass matrices for quarks and charged
leptons, as well as nearly the correct CKM matrix. An RGE analysis of the
neutrino mass parameters, including the seesaw mechanism assuming a specific
form for the right-handed neutrino mass matrix is performed, and it is found
that the neutrino mixing angles at the electroweak scale are
$\theta_{12}=35.0^{\circ}$, $\theta_{23}=47.1^{\circ}$, and
$\theta_{13}=8.27^{\circ}$. In addition,the neutrino mass-squared differences
are found to be $\Delta m^2_{32} = 0.00252$ eV$^2$ and $\Delta m^2_{21} =
0.0000739$ eV$^2$ with $m_1=0.0146$ eV, $m_2=0.0170$ eV, and $m_3=0.0530$ eV.
