  We demonstrate the emergence of an anomalous Hall effect in chiral magnetic
textures which is neither proportional to the net magnetization nor to the
well-known emergent magnetic field that is responsible for the topological Hall
effect. Instead, it appears already at linear order in the gradients of the
magnetization texture and exists for one-dimensional magnetic textures such as
domain walls and spin spirals. It receives a natural interpretation in the
language of Alain Connes' noncommutative geometry. We show that this chiral
Hall effect resembles the familiar topological Hall effect in essential
properties while its phenomenology is distinctly different. Our findings make
the re-interpretation of experimental data necessary, and offer an exciting
twist in engineering the electrical transport through magnetic skyrmions.
