  The magnetic field-induced changes in the conductivity of metals are the
subject of intense interest, both for revealing new phenomena and as a valuable
tool for determining their Fermi surface. Here, we report a hitherto unobserved
magnetoresistive effect in ultra-clean layered metals, namely a negative
longitudinal magnetoresistance that is capable of overcoming their very
pronounced orbital one. This effect is correlated with the inter-layer coupling
disappearing for fields applied along the so-called Yamaji angles where the
inter-layer coupling vanishes. Therefore, it is intrinsically associated with
the Fermi points in the field-induced quasi-one-dimensional electronic
dispersion, implying that it results from the axial anomaly among these Fermi
points. In its original formulation, the anomaly is predicted to violate
separate number conservation laws for left- and right-handed chiral- (e.g.
Weyl) fermions. Its observation in PdCoO$_2$, PtCoO$_2$ and Sr$_2$RuO$_4$
suggests that the anomaly affects the transport of clean conductors,
particularly near the quantum limit.
