We present the results of a search for doubly charged Higgs bosons (H+/-+/-) decaying to dileptons (ll(')) using approximately 240 pb(-1) of pp collision data collected by the CDF II experiment at the Fermilab Tevatron. In our search region, given by same-sign ll(') mass m(ll('))>80 GeV/c(2) (100 GeV/c(2) for ee channel), we observe no evidence for H+/-+/- production. We set limits on sigma(pp -->H++H---->l(+)l('+)l(-)l('-)) as a function of the mass of the H+/-+/- and the chirality of its couplings. Assuming exclusive same-sign dilepton decays, we derive lower mass limits on H(+/-+/-)(L) of 133, 136, and 115 GeV/c(2) in the ee, mumu, and emu channels, respectively, and a lower mass limit of 113 GeV/c(2) on H(+/-+/-)(R) in the mumu channel, all at the 95% confidence level.