Trajectory prediction is a crucial task in modeling human behavior, especially in fields as social robotics and autonomous vehicle navigation. Traditional heuristics based on handcrafted rules often lack accuracy, while recently proposed deep learning approaches suffer from computational cost, lack of explainability, and generalization issues that limit their practical adoption. In this paper, we introduce TrajEvo, a framework that leverages Large Language Models (LLMs) to automatically design trajectory prediction heuristics. TrajEvo employs an evolutionary algorithm to generate and refine prediction heuristics from past trajectory data. We introduce a Cross-Generation Elite Sampling to promote population diversity and a Statistics Feedback Loop allowing the LLM to analyze alternative predictions. Our evaluations show TrajEvo outperforms previous heuristic methods on the ETH-UCY datasets, and remarkably outperforms both heuristics and deep learning methods when generalizing to the unseen SDD dataset. TrajEvo represents a first step toward automated design of fast, explainable, and generalizable trajectory prediction heuristics. We make our source code publicly available to foster future research at https://github.com/ai4co/trajevo.