  The family of Tremblay-Turbiner-Winternitz (TTW) Hamiltonians $H_k$ on a
plane, corresponding to any positive real value of $k$, is shown to admit
another ${\cal N} = 2$ supersymmetric extension than that previously introduced
by the present author. This new extension is of the same kind as that
considered by D'Hoker and Vinet in the study of magnetic monopoles and is
characterized by the fact that all the irreducible representations of the
corresponding ${\rm osp}(2/2, \R)$ dynamical superalgebra are atypical
lowest-weight state ones. The new supersymmetric Hamiltonians may be referred
to as chiral super-TTW Hamiltonians, the role of chirality being played here by
the fermion number parity operator.
