We introduce and demonstrate a new approach to measuring coherent electron wave packets using high-harmonic spectroscopy. By preparing a molecule in a coherent superposition of electronic states, we show that electronic coherence opens previously unobserved high-harmonic-generation channels that connect distinct but coherently related electronic states. Performing the measurements in dynamically aligned nitric oxide molecules we observe the complex temporal evolution of the electronic coherence under coupling to nuclear motion. Choosing a weakly allowed transition to prepare the wave packet, we demonstrate an unprecedented sensitivity that arises from optical interference between coherent and incoherent pathways. This mechanism converts a 0.1% excitation fraction into a ∼20% signal modulation.