  For $m$ number of bosons, carrying spin ($S$=1) degree of freedom, in
$\Omega$ number of single particle orbitals, each triply degenerate, we
introduce and analyze embedded Gaussian orthogonal ensemble of random matrices
generated by random two-body interactions that are spin (S) scalar
[BEGOE(2)-$S1$]. The embedding algebra is $U(3) \supset G \supset G1 \otimes
SO(3)$ with SO(3) generating spin $S$. A method for constructing the ensembles
in fixed-($m$, $S$) space has been developed. Numerical calculations show that
the form of the fixed-($m$, $S$) density of states is close to Gaussian and
level fluctuations follow GOE. Propagation formulas for the fixed-($m$, $S$)
space energy centroids and spectral variances are derived for a general one
plus two-body Hamiltonian preserving spin. In addition to these, we also
introduce two different pairing symmetry algebras in the space defined by
BEGOE(2)-$S1$ and the structure of ground states is studied for each paring
symmetry.
