  We consider a relativistic plasma of fermions coupled to an Abelian gauge
field and carrying a chiral charge asymmetry, which might arise in the early
Universe through baryogenesis. It is known that on large length scales,
$\lambda \gtrsim 1/(\alpha \mu_5)$, the chiral anomaly opens an instability
toward the erasure of chiral charge and growth of magnetic helicity. Here the
chemical potential $\mu_{5}$ parametrizes the chiral asymmetry and $\alpha$ is
the fine-structure constant. We study the process of chiral charge erasure
through the thermal fluctuations of magnetic helicity and contrast with the
well-studied phenomenon of Chern-Simons number diffusion. Through the
fluctuation-dissipation theorem we estimate the amplitude and time scale of
helicity fluctuations on the length scale $\lambda$, finding $\delta
\mathcal{H} \sim \lambda T$ and $\tau \sim \alpha \lambda^3 T^2$ for a
relativistic plasma at temperature $T$. We argue that the presence of a chiral
asymmetry allows the helicity to grow diffusively for a time $t \sim
T^3/(\alpha^5 \mu_5^4)$ until it reaches an equilibrium value $\mathcal{H} \sim
\mu_{5} T^2 / \alpha$, and the chiral asymmetry is partially erased. If the
chiral asymmetry is small, $\mu_5 < T/\alpha$, this avenue for chiral charge
erasure is found to be slower than the chiral magnetic effect for which $t \sim
T / (\alpha^3 \mu_{5}^2)$. This mechanism for chiral charge erasure can be
important for the hypercharge sector of the Standard Model as well as
extensions including ${\rm U}(1)$ gauge interactions, such as asymmetric dark
matter models.
