Memorization is a fundamental ability of Transformer-based Large Language Models, achieved through learning. In this paper, we propose a paradigm shift by designing an architecture to memorize text directly, bearing in mind the principle that memorization precedes learning. We introduce MeMo, a novel architecture for language modeling that explicitly memorizes sequences of tokens in layered associative memories. By design, MeMo offers transparency and the possibility of model editing, including forgetting texts. We experimented with the MeMo architecture, showing the memorization power of the one-layer and the multi-layer configurations.