We demonstrate that a small transformer can learn to execute programs in MicroPy, a simplified yet computationally universal programming language. Given procedure definitions together with an expression to evaluate, the transformer predicts small-step execution using PENCIL scaffolding for space-efficient execution within a bounded context window. After training on randomly generated, semantically arbitrary MicroPy programs, the learned transformer generalizes to held-out human-written programs including bit copying and flipping, binary addition and multiplication, and SAT verification and solving. The trained model exhibits out-of-distribution generalization: it correctly evaluates programs drawn from a substantially different distribution than the one used to generate its training data. Since MicroPy can express any computation, our results provide empirical evidence that a standard transformer can be trained to act as a universal computer when paired with PENCIL scaffolding.