Materials discovery requires navigating vast chemical and structural spaces while satisfying multiple, often conflicting, objectives. We present LLM-guided Evolution for MAterials discovery (LLEMA), a unified framework that couples the scientific knowledge embedded in large language models with chemistry-informed evolutionary rules and memory-based refinement. At each iteration, an LLM proposes crystallographically specified candidates under explicit property constraints; a surrogate-augmented oracle estimates physicochemical properties; and a multi-objective scorer updates success/failure memories to guide subsequent generations. Evaluated on 14 realistic tasks that span electronics, energy, coatings, optics, and aerospace, LLEMA discovers candidates that are chemically plausible, thermodynamically stable, and property-aligned, achieving higher hit rates and improved Pareto front quality relative to generative and LLM-only baselines. Ablation studies confirm the importance of rule-guided generation, memory-based refinement, and surrogate prediction. By enforcing synthesizability and multi-objective trade-offs, LLEMA provides a principled approach to accelerating practical materials discovery. Project website: https://scientific-discovery.github.io/llema-project/