We propose to incrementally learn the segmentation of a demonstrated task into subtasks and the individual subtask policies themselves simultaneously. Previous robot learning from demonstration techniques have either learned the individual subtasks in isolation, combined known subtasks, or used knowledge of the overall task structure to perform segmentation. Our infinite mixture of experts approach instead automatically infers an appropriate partitioning (number of subtasks and assignment of data points to each one) directly from the data. We illustrate the applicability of our technique by learning a suitable set of subtasks from the demonstration of a finite-state machine robot soccer goal scorer.