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Generating editable 3D CAD geometry from natural language remains an open challenge: existing text-to-CAD systems either output surface meshes or require scarce design-history supervision, making them unsuitable for real-world engineering workflows. We introduce NURBGen, the first framework for generating high-fidelity 3D CAD models directly from natural language descriptions using Non-Uniform Rational B-Splines (NURBS). To achieve this, we fine-tune a large language model (LLM) to translate free-form texts into JSON representations containing NURBS surface parameters (\textit{i.e}, control points, knot vectors, degrees, and rational weights) which can be directly converted into BRep format using Python. Furthermore, we introduce partABC, a curated subset of the ABC dataset consisting of individual CAD components, annotated with detailed captions using an automated annotation pipeline. We further propose a hybrid representation that combines untrimmed NURBS with analytic primitives to handle trimmed surfaces and degenerate regions more robustly, while reducing token complexity. NURBGen demonstrates strong performance on diverse prompts, surpassing prior methods in geometric fidelity and dimensional accuracy, as confirmed by expert evaluations. Code and dataset will be released publicly.