Single phase, ultrafine La0.7Ca0.3MnO3 particles have been produced from polycrystalline material by mechanical grinding, consisting of crystallites of mean diameter D = 10(4) nm. The para- to ferromagnetic transition found in bulk samples at T-C = 254(2) K is barely observable in milled samples. Zero-field-cooling (ZFC) curves exhibit a maximum at T approximate to 45 K, below which irreversible behavior appears. The real part of the ac magnetic susceptibility chi'(T) showed a frequency-dependent cusp at T-m approximate to 50 K, indicating a low-temperature (reentrant) spin glass phase. The normalized shift per frequency decade was DeltaT(m)/(T-m Deltalog omega) = 0.008, close to the values for canonical spin-glasses like AuMn and CuMn. We show that Arrhenius or Vogel-Fulcher models for a thermally activated process yield unphysical results, whereas the correct determination of the freezing temperatures T-f(omega), based on the criterion tanphi = chi" /chi' = constant, solves this inconsistency. From the obtained T-f(omega) values, a dynamical analisys according to conventional critical slowing down gave T-g = 47.4(4) K and zv = 11.8(2) for SG transition temperature and dynamic exponent, respectively. These results indicate a spin-glass transition at finite temperature. Resistance measurements in zero and applied fields show semiconducting behavior, and the colossal Magnetoresistance Effect (CMR) observed in bulk samples is virtually absent. From the R(T) dependence it is inferred that those mechanisms that originate the MR at low fields, such as tunneling and spin-dependent scattering seems not to be present. We discuss this behavior and compare it with other data on related La-Sr-Mn-O and La-Ca-Mn-O systems, both bulk and nanostructured.