Coherent control of high-quality factor optical transitions in atoms has revolutionized precision frequency metrology. Leading optical atomic clocks rely on the interrogation of such transitions in either single ions or ensembles of neutral atoms to stabilize a laser frequency at high precision and accuracy. We demonstrate a platform that combines the key strengths of these two approaches, based on arrays of individual strontium atoms held within optical tweezers. We report coherence times of 3.4 seconds, single-ensemble duty cycles up to 96% through repeated interrogation, and frequency stability of 4.7 x 10(-16) (tau/s)(-1/2). These results establish optical tweezer arrays as a powerful tool for coherent control of optical transitions for metrology and quantum information science.