We present ALTO, a network orchestrator for efficiently serving compound AI systems such as pipelines of language models. ALTO leverages an optimization opportunity specific to generative language models, which is streaming intermediate outputs from the language model to downstream stages. We highlight two challenges that emerge while serving these applications at scale: handling how some stages can be stateful across partial outputs, and handling how language models can produce variable amounts of text. To address these challenges, we motivate the need for an aggregation-aware routing interface and distributed prompt-aware scheduling. ALTO's partial output streaming increases throughput by up to 3x for a fixed latency target of 4 seconds / request and reduces tail latency by 1.8x compared to a baseline serving approach, on a complex chat bot verification pipeline.