The author proves a version of I. N. Herstein's hypercenter theorem [\textit{I. N. Herstein}, J. Algebra 36, 151-157 (1975; Zbl 0313.16036)] for Lie ideals in prime rings. For any subset S in a ring R let the hypercenter of S be defined as \(H(S)=\{x\in R|\) for each \(s\in S\) there is \(n=n(x,s)>1\) so that \(xs^ n=s^ nx\}\). The result of the paper is that if R is a prime ring, char \(R\neq 2\), and R contains no nonzero nil right ideal, then for U a noncentral Lie ideal of R either H(U) is the center of R, or R embeds in \(M_ 2(F)\) for F a field. The proof is short, well written, and depends on the special case of \(U=[R,R]\) which is a consequence of a theorem of \textit{B. Felzenszwalb} and \textit{A. Giambruno} [J. Lond. Math. Soc., II. Ser. 19, 417-428 (1979; Zbl 0397.16025)].