  We use the crosscap constraint to construct open descendants of the 0B string
compactified on $T^6 /Z_3$ and on $T^4/Z_2$ free of tachyons both in the closed
and in the open unoriented sectors. In four dimensions the construction results
in a Chan-Paton gauge group $U(8)\otimes U(12)\otimes U(12)$ with three
generations of chiral fermions in the representations
$(\overline{8},1,\overline{12}) +(8,12,1)+(1,\overline{66},1)+(1,1,66)$.
