  The main result established in this paper is the existence and uniqueness of
strong solutions to the obstacle problem for a class of subelliptic operators
in non-divergence form. The operators considered are structured on a set of
smooth vector fields in R^n; X = \{X_0, X_1, ...,X_q\}, q \le n, satisfying
H\"ormanders finite rank condition. In this setting, X_0 is a lower order term
while {X1, ...,X_q} are building blocks of the subelliptic part of the
operator. In order to prove this, we establish an embedding theorem under the
assumption that the set {X_0, X_1, ...,X_q} generates a homogeneous Lie group.
Furthermore, we prove that any strong solution belongs to a suitable class of
H\"older continuous functions.
