This note is about a certain 16-dimensional family of surfaces of general type with $p_g=2$ and $q=0$ and $k^2=1$, called “special Horikawa surfaces”. These surfaces, studied by Pearlstein–Zhang and by Garbagnati, are related to $K_3$ surfaces. We show that special Horikawa surfaces have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, the Chow ring of special Horikawa surfaces displays $K_3$-like behavior.