  In this paper, by applying a linear trace Li-Yau-Hamilton inequality for a
positive (1,1)-form solution of the CR Hodge-Laplace heat equation and
monotonicity of the heat equation deformation, we obtain an optimal gap theorem
for a complete strictly pseudocovex CR manifold with nonnegative
pseudohermitian bisectional curvature and vanishing torsion. We prove that if
the average of the Tanaka-Webster scalar curvature over a ball of radius
centered at some point o decays as $o(r^{-2})$, then the manifold is flat.
