If dwarf galaxies are primeval objects in the universe, as hierarchical galaxy formation scenarios predict, they should show traces of their old stellar populations, perhaps distributed in extended, differentiated structures. The working hypothesis that such a structure could exist is tested for the case of DDO 187, a field, dwarf irregular galaxy showing a high gas fraction and low metallicity. For this purpose, the structure, star formation history, and other properties of the galaxy are analyzed using the spatial distribution of stars, the color-magnitude diagrams of about 1500 resolved stars, and the fluxes of H II regions, together with data about the gas distribution. From the I magnitude of the tip of the red giant branch (ITRGB), the distance of DDO 187 to the Milky Way is estimated to be 2.5+/-0.2 Mpc. The distance to several neighbor galaxies and groups has been computed, showing that DDO 187 is probably an isolated, field galaxy. The distance of DDO 187 to the Milky Way is almost 3 times smaller than that obtained from Cepheid light curves. Considering that this is the third case in which such a large disagreement is detected, it seems clear that Cepheid distance estimates based on a few stars, as usually happens in dwarf galaxies, must be accepted with caution. The star formation history of DDO 187 has been analyzed. The central region of DDO 187 shows an overall time decreasing star formation rate with a strong burst in its central region that happened between 20 and 100 Myr ago and a present-day star formation activity 3 times smaller than the maximum one. Besides this, a spatially extended stellar component has been found that has no young stars and exceeds the size of the gas component. In short, several results suggest that DDO 187 has a two-component, halo/disk-like structure: (1) differentiated morphologies for the inner (flat) and outer (spheroidal) stellar components, (2) a gas component less extended than the outer stellar component, and (3) an outer component lacking young stars, which are abundant in the inner component. The working hypothesis that a real halo/disk structure could be present is discussed. The conclusion is reached that the two-component hypothesis is not unrealistic, but nothing can be definitely stated until more detailed data, ideally including kinematics, are available.