  We calculate the two-loop contributions from a modified trilinear Higgs
self-interaction, $\kappa_\lambda \lambda_{\rm SM} v h^3$, to the electroweak
oblique parameters $S$ and $T$. Using the current bounds on $S$ and $T$ from
electroweak measurements, we find the 95% C.L. constraint on the modified
trilinear coupling to be $-14.0 \leq \kappa_\lambda \leq 17.4$. The largest
effects on $S$ and $T$ arise from two insertions of the modified trilinear
coupling that result in $T/ S \simeq -3/2$; remarkably, this is nearly parallel
to the axis of the tightest experimental constraint in the $S$-$T$ plane. No
contributions to $S$ and $T$ arise from a modified Higgs quartic coupling at
two-loop order. These calculations utilized a gauge-invariant parameterization
of the trilinear Higgs coupling in terms of higher dimensional operators
$(H^\dagger H)^{n}$ with $n \ge 3$. Interestingly, the bounds on
$\kappa_\lambda$ that we obtain are comparable to constraints from di-Higgs
production at the LHC as well as recent bounds from single Higgs production at
the LHC.
