Recently, large-scale pre-trained Vision and Language (VL) models have set a new state-of-the-art (SOTA) in zero-shot visual classification enabling open-vocabulary recognition of potentially unlimited set of categories defined as simple language prompts. However, despite these great advances, the performance of these zero-shot classifiers still falls short of the results of dedicated (closed category set) classifiers trained with supervised fine-tuning. In this paper we show, for the first time, how to reduce this gap without any labels and without any paired VL data, using an unlabeled image collection and a set of texts auto-generated using a Large Language Model (LLM) describing the categories of interest and effectively substituting labeled visual instances of those categories. Using our label-free approach, we are able to attain significant performance improvements over the zero-shot performance of the base VL model and other contemporary methods and baselines on a wide variety of datasets, demonstrating absolute improvement of up to $11.7\%$ ($3.8\%$ on average) in the label-free setting. Moreover, despite our approach being label-free, we observe $1.3\%$ average gains over leading few-shot prompting baselines that do use 5-shot supervision.