  We revisit the role of the chiral "triangle" anomaly in deeply inelastic
scattering (DIS) of electrons off polarized protons employing a powerful
worldline formalism. We demonstrate how the triangle anomaly appears at high
energies in the DIS box diagram for the polarized proton structure function
$g_1(x_B,Q^2)$ in both the Bjorken limit of large $Q^2$ and in the Regge limit
of small $x_B$. We show that the operator product expansion is not required to
extract the anomaly in either asymptotics though it is sufficient in the
Bjorken limit. Likewise, the infrared pole in the anomaly arises in both
limits. The leading contribution to $g_1$, in both Bjorken and Regge
asymptotics, is therefore given by the expectation value of the topological
charge density, generalizing a result previously argued by Jaffe and Manohar to
hold for the first moment of $g_1$. In follow-up work, we will show how our
results motivate the derivation of a helicity-dependent effective action
incorporating the physics of the anomaly at small $x_B$ and shall discuss the
QCD evolution of $g_1(x_B,Q^2)$ in this framework.
