Factors that influence speciation rates among groups of organisms are integral to deciphering macroevolutionary processes; however, they remain poorly understood. Here, we use molecular phylogenetic data and divergence time estimates to reconstruct the pattern and tempo of speciation within a widespread and homogeneous bird family (white-eyes, Zosteropidae) that contains an archetypal "great speciator." Our analyses show that the majority of this species-rich family constitutes a clade that arose within the last 2 million years, yielding a per-lineage diversification rate among the highest reported for vertebrates (1.95-2.63 species per million years). However, unlike most rapid radiations reported to date, this burst of diversification was not limited in geographic scope, but instead spanned the entire Old World tropics, parts of temperate Asia, and numerous Atlantic, Pacific, and Indian Ocean archipelagos. The tempo and geographic breadth of this rapid radiation defy any single diversification paradigm, but implicate a prominent role for lineage-specific life-history traits (such as rapid evolutionary shifts in dispersal ability) that enabled white-eyes to respond rapidly and persistently to the geographic drivers of diversification.