  We study conditions on general fluxes of massive Type IIA supergravity that
lead to four-dimensional backgrounds with N = 1 supersymmetry. We derive these
conditions in the case of SU(3)- as well as SU(2)-structures. SU(3)-structures
imply that the internal space is constrained to be a nearly K\"ahler manifold
with all the turned on fluxes, and the negative cosmological constant
proportional to the mass parameter, and the dilaton fixed by the quantized
ratio of the three-form and four-form fluxes. We further discuss the
implications of such flux vacua with added intersecting D6-branes, leading to
the chiral non-Abelian gauge sectors (without orientifold projections).
Examples that break SU(3)-structures to SU(2)-ones allow for the internal space
conformally flat (up to orbifold and orientifold projections), for which we
give an explicit example. These results provide a starting point for further
study of the four-dimensional (chiral) N = 1 supersymmetric solutions of
massive Type IIA supergravity with D-branes and fluxes, compactified on
orientifolds.
