  We show that certain Fano eightfolds (obtained as hyperplane sections of an
orthogonal Grassmannian, and studied by Ito-Miura-Okawa-Ueda and by
Fatighenti-Mongardi) have a multiplicative Chow-K\"unneth decomposition. As a
corollary, the Chow ring of these eightfolds behaves like that of K3 surfaces.
