N-Version Programming is a well-known methodology for developing fault-tolerant systems. It achieves fault detection and correction at runtime by adding diverse redundancy into programs, minimizing fault mode overlap between redundant program variants. In this work, we propose the automated generation of program variants using large language models. We design, develop, and evaluate Galápagos: a tool for generating program variants using LLMs, validating their correctness and equivalence, and using them to assemble N-Version binaries. We evaluate Galápagos by creating N-Version components of real-world C code. Our original results show that Galápagos can produce program variants that are proven to be functionally equivalent, even when the variants are written in a different programming language. Our systematic diversity measurement indicates that functionally equivalent variants produced by Galápagos are statically different after compilation and present diverging internal behavior at runtime. We demonstrate that the variants produced by Galápagos can protect C code against real miscompilation bugs which affect the Clang compiler. Overall, our article shows that producing N-Version software can be drastically automated by advanced usage of practical formal verification and generative language models.