Communication has become a first-order bottleneck in large-scale GPU workloads, and existing distributed compilers address it mainly by overlapping whole compute and communication kernels at the stream level. This coarse granularity incurs extra kernel launches, forces device-wide synchronizations at kernel boundaries, and leaves substantial slack when the slowest tile or kernel stretches the communication tail. We present Syncopate, a compiler and runtime that enables automatic fine-grained overlap inside a single fused kernel. Syncopate introduces a communication chunk abstraction that decouples communication granularity from kernel structure and backend mechanisms, allowing chunk-level plans to be ported from existing distributed compilers, written directly by users, or instantiated from reusable templates. Given a local Triton kernel and a chunk schedule, Syncopate performs transformations to align computation with chunk availability. Implemented as a source-to-source compiler on Triton, Syncopate delivers an average end-to-end speedup of 1.3$\times$ and up to 4.7$\times$ on multi-GPU workloads. Our code is open-sourced at https://github.com/tie-pilot-qxw/syncopate.