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During development, neurons arrive at local brain areas in an extended period of time, but how they form local neural circuits is unknown. Here we computationally model the emergence of a network for precise timing in the premotor nucleus HVC in songbird. We show that new projection neurons, added to HVC post hatch at early stages of song development, are recruited to the end of a growing feedforward network. High spontaneous activity of the new neurons makes them the prime targets for recruitment in a self-organized process via synaptic plasticity. Once recruited, the new neurons fire readily at precise times, and they become mature. Neurons that are not recruited become silent and replaced by new immature neurons. Our model incorporates realistic HVC features such as interneurons, spatial distributions of neurons, and distributed axonal delays. The model predicts that the birth order of the projection neurons correlates with their burst timing during the song.