  We investigate a model of Dirac fermions with Haldane type mass impurities
which open a global topological gap even in the dilute limit. Surprisingly, we
find that the chirality of this mass term, i.e., the sign of the Chern number,
can be reversed by tuning the magnitude of the single-impurity scattering.
Consequently, the disorder induces a phase disconnected from the clean
topological phase, i.e., a genuine topological Anderson insulator. In seeming
contradiction to the expectation that mass disorder is an irrelevant
perturbation to the clean integer quantum Hall transition, the tri-critical
point separating these two Chern insulating phases and a thermal metal phase is
located at zero impurity density and connected to the appearance of a zero
energy bound state in the continuum corresponding to a divergent Haldane mass
impurity. Our conclusions based on the T-matrix expansion are substantiated by
large scale Chebyshev-Polynomial-Green-Function numerics. We discuss possible
experimental platforms.
