While there has been plenty of work on generating tests from existing code, there has been limited work on generating tests from issues. A correct test must validate the code patch that resolves the issue. This paper focuses on the scenario where that code patch does not yet exist. Doing so supports two major use-cases. First, it supports TDD (test-driven development), the discipline of "test first, write code later" that has well-documented benefits for human software engineers. Second, it also validates SWE (software engineering) agents, which generate code patches for resolving issues. This paper introduces TDD-Bench-Verified, a benchmark for generating tests from issues, and Otter, an LLM-based solution for this task. Otter augments LLMs with rule-based analysis to check and repair their outputs, and introduces a novel self-reflective action planner. Experiments show Otter outperforming state-of-the-art systems for generating tests from issues, in addition to enhancing systems that generate patches from issues. We hope that Otter helps make developers more productive at resolving issues and leads to more robust, well-tested code.