  Let H be the Hermite operator -\Delta +|x|^2 on \mathbb{R}^n. We prove a
weighted L^2 estimate of the maximal commutator operator \sup_{R>0}|[b,
S_R^\lambda(H)](f)|, where [b, S_R^\lambda(H)](f) = bS_R^\lambda(H) f -
S_R^\lambda(H)(bf) is the commutator of a BMO function b and the Bochner-Riesz
means S_R^\lambda(H) for the Hermite operator H. As an application, we obtain
the almost everywhere convergence of [b, S_R^\lambda(H)](f) for large \lambda
and f\in L^p(\mathbb{R}^n).
