  In this paper we provide an explicit bound for $|\zeta(1+it)|$ in the form of
$|\zeta(1+it)|\leq \min\left(\log t, \frac{1}{2}\log t+1.93, \frac{1}{5}\log
t+44.02 \right)$. This improves on the current best-known explicit bound of
$|\zeta(1+it)|\leq 62.6(\log t)^{2/3}$ up until $t$ of the magnitude
$10^{10^7}$.
