  Inspired by the recent experimental observation of topological
superconductivity in ferromagnetic chains, we consider a dilute 2D lattice of
magnetic atoms deposited on top of a superconducting surface with a Rashba
spin-orbit coupling. We show that the studied system supports a generalization
of $p_x+ip_y$ superconductivity and that its topological phase diagram contains
Chern numbers higher than $\xi/a$ $(\gg1)$, where $\xi$ is the superconducting
coherence length and $a$ is the distance between the magnetic atoms. The
signatures of nontrivial topology can be observed by STM spectroscopy in
finite-size islands.
