This paper proposes a novel biomimetic Carbon Fibre Reinforced Polymer (CFRP) with a microstructure inspired by fish scales. The aim of the novel microstructure is to improve the perforation resistance of CFRP without compromising its flexibility. To this end, we prototype the first ever CFRP laminate with scales and test it in quasi-static indentation on a soft backing material. We compare the mechanical behaviour of the CFRP with scales to two baseline configurations with conventional lay-ups. The results presented in this paper suggest that the CFRP with scales significantly outperforms the two baseline configurations in terms of force and displacement at penetration, while being flexible. This makes CFRPs with scales an attractive alternative for applications where perforation resistance is paramount, such as body armour against low velocity strikes.