We present the results of a search for doubly-charged Higgs bosons (H+/-+/-) decaying to dileptons using ~240/pb of ppbar collision data collected by the CDF II experiment at the Fermilab Tevatron. In our search region, given by same-sign dilepton mass m_ll' > 80 GeV/c^2 (100 GeV/c^2 for dielectron channel), we observe no evidence for doubly-charged Higgs production. We set limits on sigma (ppbar --> H++H-- --> l+l+l-l-) as a function of the mass of the doubly-charged Higgs boson and the chirality of its couplings. Assuming exclusive same-sign dilepton decays, we derive lower mass limits on H+/-+/-_L of 133 GeV/c^2, 136 GeV/c^2, and 115 GeV/c^2 in the ee, mu mu, and e mu channels, respectively, and a lower mass limit of 113 GeV/c^2 on H+/-+/-_R in the mu mu channel, all at the 95% confidence level.

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