  We study the difficulties associated with detecting chiral singularities
predicted by chiral perturbation theory (ChPT) in lattice QCD. We focus on the
physics of the remnant O(2) chiral symmetry of staggered fermions in the strong
coupling limit using the recently discovered directed path algorithm. Since it
is easier to look for power-like singularities as compared to logarithmic ones,
our calculations are performed at a fixed finite temperature in the chirally
broken phase. We show that the behavior of the chiral condensate, the pion mass
and the pion decay constant, for small masses, are all consistent with the
predictions of ChPT.
  However, the values of the quark masses that we need to demonstrate this are
much smaller than those being used in dynamical QCD simulations. We also need
to use higher order terms in the chiral expansion to fit our data.
