Species richness is an important characteristic of ecological communities, but it is difficult to quantify. We report here a thorough inventory of a tropical rain forest ant fauna and use it to evaluate species richness estimators. The study was carried out in ;1500 ha of lowland rain forest at La Selva Biological Station, Costa Rica. Diverse methods were used, including canopy fogging, Malaise traps, Berlese samples, Winkler samples, baiting, and manual search. Workers of 437 ant species were encountered. The abundance distribution was clearly lognormal, and the distribution emerged from a veil line with each doubling of sampling effort. Three richness estimates were calculated: the area under the fitted lognormal distribution, the asymptote of the Michaelis-Menten equation fit to the species accumulation curve, and the Incidence-based Coverage Estimator (ICE). The performance of the estimators was evaluated with sample-based rarefaction plots. The inventory was nearly complete because the species accumulation curve approached an asymptote, the richness estimates were very close to the observed species richness, and the uniques and duplicates curves were both declining. None of the richness estimators was stable in samplebased rarefaction plots, but regions of stability of estimators occurred. The explanation of rarity is one key to understanding why richness estimates fail. Fifty-one species (12% of the total) were still uniques (known from only one sample) at the end of the inventory. The rarity of 20 of these species was explained by ‘‘edge effects’’: ‘‘methodological edge species’’ (possibly abundant at the site but difficult to sample because of their microhabitat), and ‘‘geographic edge species,’’ known to be common in habitats or regions outside of La Selva. Rarity of 31 species remained unexplained. Most of the 51 rare species were known from additional collections outside of La Selva, either in other parts of Costa Rica or in other countries. Only six species were ‘‘global uniques,’’ known to date from only one sample on Earth. The study demonstrates that patterns of species occurrence early in an inventory may be inadequate to estimate species richness, but that relatively complete inventories of species-rich arthropod communities are possible if multiple sampling methods and extensive effort are applied.