Learning while asleep is a dream of mankind, but is often deemed impossible because sleep lacks the conscious awareness and neurochemical milieu thought to be necessary for learning. Current evidence for sleep learning in humans is inconclusive. To explore conditions under which verbal learning might occur, we hypothesized that peaks of slow waves would be conducive to verbal learning because the peaks define periods of neural excitability. While in slow-wave sleep during a nap, a series of word pairs comprising pseudowords, e.g., “tofer,” and actual German words, e.g., “Haus” (house), were played to young German-speaking women and men. When the presentation of the second word of a pair (e.g., “Haus” of “tofer-house”) coincided with an ongoing slow-wave peak, the chances increased that a new semantic association between the pair had been formed and retained. Sleep-formed associations translated into awake ones, where they guided forced choices on an implicit memory test. Reactivations of sleep-formed associations were mirrored by brain activation increases measured with fMRI in cortical language areas and the hippocampus, a brain structure critical for relational binding. We infer that implicit relational binding had occurred during peaks of slow oscillations, recruiting a hippocampal-neocortical network comparable to vocabulary learning in the waking state.