This paper provides a survey of the emerging area of Large Language Models (LLMs) for Software Engineering (SE). It also sets out open research challenges for the application of LLMs to technical problems faced by software engineers. LLMs' emergent properties bring novelty and creativity with applications right across the spectrum of Software Engineering activities including coding, design, requirements, repair, refactoring, performance improvement, documentation and analytics. However, these very same emergent properties also pose significant technical challenges; we need techniques that can reliably weed out incorrect solutions, such as hallucinations. Our survey reveals the pivotal role that hybrid techniques (traditional SE plus LLMs) have to play in the development and deployment of reliable, efficient and effective LLM-based SE.