Marine planktonic microfossils have provided some of the best examples of evolutionary rates and patterns on multi-million-year time scales, including many instances of gradual evolution. Lineage splitting as a result of speciation has also been claimed, but all such studies have used subjective visual species discrimination, and interpretation has often been complicated by relatively small sample sizes and oceanographic complexity at the study sites. Here we analyze measurements on a collection of 10,200 individual tests of the Eocene planktonic foraminifer Turborotalia in 51 stratigraphically ordered samples from a site within the oceanographically stable tropical North Pacific gyre. We use novel multivariate statistical clustering methods to test the hypothesis that a single evolutionary species was present from 45 Ma to its extinction ca. 34 Ma. After identification of a set of biologically relevant traits, the protocol we apply does not require a prior assignment of individuals to species. We find that for most of the record, contemporaneous specimens form one morphological cluster, which we interpret as an evolving species that shows quasi-continuous but non-directional gradual evolutionary change (anagenesis). However, in the upper Eocene from ca. 36 to ca. 34 Ma there are two clusters that persistently occupy distinct areas of morphospace, from which we infer that speciation (cladogenesis) must have occurred.