This paper introduces the first \emph{self-evolving} logic synthesis framework, which leverages Large Language Model (LLM) agents to autonomously improve the source code of \textsc{ABC}, the widely adopted logic synthesis system. Our framework operates on the \emph{entire integrated ABC codebase}, and the output repository preserves its single-binary execution model and command interface. In the initial evolution cycle, we bootstrap the system using existing prior open-source synthesis components, covering flow tuning, logic minimization, and technology mapping, but without manually injecting new heuristics. On top of this foundation, a team of LLM-based agents iteratively rewrites and evolves specific sub-components of ABC following our ``programming guidance`` prompts under a unified correctness and QoR-driven evaluation loop. Each evolution cycle proposes code modifications, compiles the integrated binary, validates correctness, and evaluates quality-of-results (QoR) on \emph{multi-suite benchmarks including ISCAS~85/89/99, VTR, EPFL, and IWLS~2005}. Through continuous feedback, the system discovers optimizations beyond human-designed heuristics, effectively \emph{learning new synthesis strategies} that enhance QoR. We detail the architecture of this self-improving system, its integration with \textsc{ABC}, and results demonstrating that the framework can autonomously and progressively improve EDA tool at full million-line scale.