I'm not quite sure this is what you want, but, for massless particles, so the 3-momentum cannot vanish, you can define, in any frame, $\hat p\equiv \vec p /|\vec p|$; hence, you have
$$
h=\hat p \cdot \vec S= \frac{1}{2} \gamma^0 \gamma^5 \vec \gamma \cdot \hat p.
$$
But this manifestly commutes with chirality, $\gamma^5$, so the two operators share eigenvectors.
Left-chiral ones have negative helicity, and right-chiral ones positive helicity. The numerical magnitude of eigenvalues is irrelevant here: The article focusses on the sign of the helicity.
For more details of how Dirac equation spinors realize the above for both particles and antiparticles, see here. Note how a fermion reverses chirality, spin and helicity upon charge conjugation.