We present a search for associated Higgs boson production in the process $p\bar{p} \to WH\to WWW^*\to l^\pm\nu l'^\pm\nu'+X$ in final states containing two like-sign isolated electrons or muons ($e^\pm e^\pm$, $e^\pm \mu^\pm$, or $\mu^\pm \mu^\pm$). The search is based on D0 Run II data samples corresponding to integrated luminosities of 360--380 pb$^{-1}$. No excess is observed over the predicted standard model background. We set 95% C.L. upper limits on $\sigma(p\bar{p}\to WH)\times Br(H\to WW^*)$ between 3.2 and 2.8 pb for Higgs masses from 115 to 175 GeV.

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