The star formation history (SFH) of Local Group galaxies is a powerful tool for studying their evolution, including chemical enrichment histories and stellar population gradients, which in turn may shed light on the role of reionization or Supernovae feedback in galaxy formation and evolution. In particular, isolated dwarfs are ideal laboratories since their evolution has not been complicated by the vicinity of giant galaxies. In this paper, we present the project Local Cosmology from Isolated Dwarfs (LCID), aimed at deriving detailed SFHs for a sample of Local Group isolated dwarf galaxies. To accomplish this goal we have collected, using the ACS on board the HST, color-magnitude diagrams (CMD) reaching their oldest main sequence turnoff (V~28 or M_V~+3.5) with good photometric accuracy. Some preliminary results from the CMDs are shown and briefly discussed.