  Models that lead to a cosmological stiff fluid component, with a density
$\rho_S$ that scales as $a^{-6}$, where $a$ is the scale factor, have been
proposed recently in a variety of contexts. We calculate numerically the effect
of such a stiff fluid on the primordial element abundances. Because the stiff
fluid energy density decreases with the scale factor more rapidly than
radiation, it produces a relatively larger change in the primordial helium-4
abundance than in the other element abundances, relative to the changes
produced by an additional radiation component. We show that the helium-4
abundance varies linearly with the density of the stiff fluid at a fixed
fiducial temperature. Taking $\rho_{S10}$ and $\rho_{R10}$ to be the stiff
fluid energy density and the standard density in relativistic particles,
respectively, at $T = 10$ MeV, we find that the change in the primordial helium
abundance is well-fit by $\Delta Y_p = 0.00024(\rho_{S10}/\rho_{R10})$. The
changes in the helium-4 abundance produced by additional radiation or by a
stiff fluid are identical when these two components have equal density at a
"pivot temperature", $T_*$, where we find $T_* = 0.55$ MeV. Current estimates
of the primordial $^4$He abundance give the constraint on a stiff fluid energy
density of $\rho_{S10}/\rho_{R10} < 30$.
