Fully Homomorphic Encryption (FHE) enables ofoading computation to untrusted servers with cryptographic privacy. Despite its attractive security, FHE is not yet widely adopted due to its prohibitive overheads, about 10,000× over unencrypted computation. Recent FHE accelerators have made strides to bridge this performance gap. Unfortunately, prior accelerators only work well for simple programs, but become inefcient for complex programs, which bring additional costs and challenges. We present CraterLake, the frst FHE accelerator that enables FHE programs of unbounded size (i.e., unbounded multiplicative depth). Such computations require very large ciphertexts (tens of MBs each) and different algorithms that prior work does not support well. To tackle this challenge, CraterLake introduces a new hardware architecture that efciently scales to very large ciphertexts, novel functional units to accelerate key kernels, and new algorithms and compiler techniques to reduce data movement. We evaluate CraterLake on deep FHE programs, including deep neural networks like ResNet and LSTMs, where prior work takes minutes to hours per inference on a CPU. CraterLake outperforms a CPU by gmean 4,600× and the best prior FHE accelerator by 11.2× under similar area and power budgets. These speeds enable realtime performance on unbounded FHE programs for the frst time.