There is an overwhelming archeological and genetic evidence that modern speech apparatus was acquired by hominins by 600,000 years ago. On the other hand, artifacts signifying modern imagination, such as (1) composite figurative arts, (2) bone needles with an eye, (3) construction of dwellings, and (4) elaborate burials arose not earlier than 70,000 years ago. It remains unclear (1) why there was a long gap between acquisition of modern speech apparatus and modern imagination, (2) what triggered the acquisition of modern imagination 70,000 years ago, and (3) what role language might have played in this process. Our research into evolutionary origin of modern imagination has been driven by the observation of a temporal limit for the development of a particular component of imagination. Modern children not exposed to recursive language in early childhood never acquire the type of active constructive imagination called Prefrontal Synthesis (PFS). Unlike vocabulary and grammar acquisition, which can be learned throughout one’s lifetime, there is a strong critical period for the development of PFS and individuals not exposed to recursive language in early childhood can never acquire PFS as adults. Their language will always lack understanding of spatial prepositions and recursion that depend on the PFS ability. In a similar manner, early hominins would not have been able to learn recursive language as adults and, therefore, would not be able to teach recursive language to their children. Thus, the existence of a strong critical period for PFS acquisition creates an evolutionary barrier for behavioral modernity. An evolutionary mathematical model suggests that a synergistic confluence of three events (1) a genetic mutation that extended the critical period by slowing down the prefrontal cortex development simultaneously in two or more children, (2) invention of recursive elements of language, such as spatial prepositions, by these children and (3) their dialogic communications using these recursive elements, resulted in concurrent conversion of a non-recursive communication system of their parents to recursive language and acquisition of PFS around 70,000 years ago.