Directed evolution is a powerful approach for engineering biomolecules and understanding adaptation. However, experimental strategies for directed evolution are notoriously labor intensive and low throughput, limiting access to demanding functions, multiple functions in parallel, and the study of molecular evolution in replicate. We report OrthoRep, an orthogonal DNA polymerase-plasmid pair in yeast that stably mutates ∼100,000-fold faster than the host genome in vivo, exceeding the error threshold of genomic replication that causes single-generation extinction. User-defined genes in OrthoRep continuously and rapidly evolve through serial passaging, a highly straightforward and scalable process. Using OrthoRep, we evolved drug-resistant malarial dihydrofolate reductases (DHFRs) in 90 independent replicates. We uncovered a more complex fitness landscape than previously realized, including common adaptive trajectories constrained by epistasis, rare outcomes that avoid a frequent early adaptive mutation, and a suboptimal fitness peak that occasionally traps evolving populations. OrthoRep enables a new paradigm of routine, high-throughput evolution of biomolecular and cellular function.