  Due to their topological charge, or chirality, the Weyl cones present in
topological semimetals are considered robust against arbitrary perturbations.
One well-understood exception to this robustness is the pairwise creation or
annihilation of Weyl cones, which involves the overlap of two oppositely
charged nodes in energy and momentum. Here we show that their topological
charge can in fact change sign, in a process that involves the merging of not
two, but three Weyl nodes. This is facilitated by the presence of rotation and
time-reversal symmetries, which constrain the relative positions of Weyl cones
in momentum space. We analyze the chirality flip process, showing that
transport properties distinguish it from the conventional, double Weyl merging.
Moreover, we predict that the chirality flip occurs in MoTe$_2$, where
experimentally accessible strain leads to the merging of three Weyl cones close
to the Fermi level. Our work sets the stage to further investigate and observe
such chirality flipping processes in different topological materials.
