Large language model agents demonstrate expert-level reasoning, yet consistently fail on enterprise-specific tasks due to missing domain knowledge -- terminology, operational procedures, system interdependencies, and institutional decisions that exist largely as tribal knowledge. Current approaches fall into two categories: top-down knowledge engineering, which documents domain knowledge before agents use it, and bottom-up automation, where agents learn from task experience. Both have fundamental limitations: top-down efforts produce bloated, untested knowledge bases; bottom-up approaches cannot acquire knowledge that exists only in human heads. We present Demand-Driven Context (DDC), a problem-first methodology that uses agent failure as the primary signal for what domain knowledge to curate. Inspired by Test-Driven Development, DDC inverts knowledge engineering: instead of curating knowledge and hoping it is useful, DDC gives agents real problems, lets them demand the context they need, and curates only the minimum knowledge required to succeed. We describe the methodology, its entity meta-model, and a convergence hypothesis suggesting that 20-30 problem cycles produce a knowledge base sufficient for a given domain role. We demonstrate DDC through a worked example in retail order fulfillment, where nine cycles targeting an SRE incident management agent produce a reusable knowledge base of 46 entities. Finally, we propose a scaling architecture for enterprise adoption with semi-automated curation and human governance.