  A supersymmetric extension of the nonlinear O(3) sigma model in two spacetime
dimensions is investigated by means of Monte Carlo simulations. We argue that
it is impossible to construct a lattice action that implements both the O(3)
symmetry as well as at least one supersymmetry exactly at finite lattice
spacing. It is shown by explicit calculations that previously proposed
discretizations fail to reproduce the exact symmetries of the target manifold
in the continuum limit. We provide an alternative lattice action with exact
O(3) symmetry and compare two approaches based on different derivative
operators. Using the nonlocal SLAC derivative for the quenched model on
moderately sized lattices we extract the value {\sigma}(2, u_0) = 1.2604(13)
for the step scaling function at u_0 = 1.0595, to be compared with the exact
value 1.261210. For the supersymmetric model with SLAC derivative the discrete
chiral symmetry is maintained but we encounter strong sign fluctuations,
rendering large lattice simulations ineffective. By applying the Wilson
prescription, supersymmetry and chiral symmetry are broken explicitly at finite
lattice spacing, though there is clear evidence that both are restored in the
continuum limit by fine tuning of a single mass parameter.
