We introduce COOL-CHIC, a Coordinate-based Low Complexity Hierarchical Image Codec. It is a learned alternative to autoencoders with approximately 2000 parameters and 2500 multiplications per decoded pixel. Despite its low complexity, COOL-CHIC offers compression performance close to modern conventional MPEG codecs such as HEVC and VVC. This method is inspired by the Coordinate-based Neural Representation, where an image is represented as a learned function which maps pixel coordinates to RGB values. The parameters of the mapping function are then sent using entropy coding. At the receiver side, the compressed image is obtained by evaluating the mapping function for all pixel coordinates. COOL-CHIC implementation is made available upon request.