  Topological states of matter, such as fractional quantum Hall states, are an
active field of research due to their exotic excitations. In particular,
ultracold atoms in optical lattices provide a highly controllable and adaptable
platform to study such new types of quantum matter. However, finding a clear
route to realize non-Abelian quantum Hall states in these systems remains
challenging. Here we use the density-matrix renormalization-group (DMRG) method
to study the Hofstadter-Bose-Hubbard model at filling factor $\nu = 1$ and find
strong indications that at $\alpha=1/6$ magnetic flux quanta per plaquette the
ground state is a lattice analog of the continuum non-Abelian Pfaffian. We
study the on-site correlations of the ground state, which indicate its paired
nature at $\nu = 1$, and find an incompressible state characterized by a charge
gap in the bulk. We argue that the emergence of a charge density wave on thin
cylinders and the behavior of the two- and three-particle correlation functions
at short distances provide evidence for the state being closely related to the
continuum Pfaffian. The signatures discussed in this letter are accessible in
current cold atom experiments and we show that the Pfaffian-like state is
readily realizable in few-body systems using adiabatic preparation schemes.
