  Let $A$ be a brace algebra. This structure implies that $A$ is also a pre-Lie
algebra. In this paper, we establish Composition-Diamond lemma for brace
algebras. Using this Composition-Diamond lemma we prove that each pre-Lie
algebra $L$ can be embedded into a brace algebra $A_L$, i.e., $L$ is a pre-Lie
subalgebra of $A_L$ up to isomorphism. We also determine an explicit linear
basis for the brace algebra $A_{L}$.
