A series of experiments explored whether chunking in short-term memory for verbal materials depends on attentionally limited executive processes. Secondary tasks were used to disrupt components of working memory and chunking was indexed by the sentence superiority effect, whereby immediate recall is better for sentences than word lists. To facilitate comparisons and maximise demands on working memory, materials were constrained by re-sampling a small set of words. Experiment 1 confirmed a reliable sentence superiority effect with constrained materials. Experiment 2 showed that secondary tasks of concurrent articulation and visual choice reaction impaired recall, but did not remove or reduce the sentence superiority effect. This was also the case with visual and verbal n-back concurrent tasks (Experiment 3), and with concurrent backward counting (Experiment 4). Backward counting did however interact with mode of presenting the memory materials, suggesting that our failure to find interactions between concurrent task and materials was not attributable to our methodology. We conclude that executive processes are not crucial for the sentence chunking advantage and we discuss implications for the episodic buffer and other theoretical accounts of working memory and chunking. (Contains 5 tables and 6 figures.)