  We define a modified dimensional-regularization technique that overcomes
several difficulties of the ordinary technique, and is specially designed to
work efficiently in chiral and parity violating quantum field theories, in
arbitrary dimensions greater than 2. When the dimension of spacetime is
continued to complex values, spinors, vectors and tensors keep the components
they have in the physical dimension, therefore the $\gamma $ matrices are the
standard ones. Propagators are regularized with the help of evanescent
higher-derivative kinetic terms, which are of the Majorana type in the case of
chiral fermions. If the new terms are organized in a clever way, weighted power
counting provides an efficient control on the renormalization of the theory,
and allows us to show that the resulting chiral dimensional regularization is
consistent to all orders. The new technique considerably simplifies the proofs
of properties that hold to all orders, and makes them suitable to be
generalized to wider classes of models. Typical examples are the
renormalizability of chiral gauge theories and the Adler-Bardeen theorem. The
difficulty of explicit computations, on the other hand, may increase.
