  Hot gas in filamentary structures induces CMB aniostropy through the SZ
effect. Guided by results from N-body simulations, we model the morphology and
gas properties of filamentary gas and determine the power spectrum of the
anisotropy. Our treatment suggests that power levels can be an appreciable
fraction of the cluster contribution at multipoles $\ell\lesssim 1500$. Its
spatially irregular morphology and larger characteristic angular scales can
help to distinguish this SZ signature from that of clusters. In addition to
intrinsic interest in this most extended SZ signal as a probe of filaments, its
impact on cosmological parameter estimation should also be assessed. We find
that filament `noise' can potentially bias determination of $A_s$, $n_s$, and
$w$ (the normalization of the primordial power spectrum, the scalar index, and
the dark energy equation of state parameter, respectively) by more than the
nominal statistical uncertainty in Planck SZ survey data. More generally, when
inferred from future optimal cosmic-variance-limited CMB experiments, we find
that virtually all parameters will be biased by more than the nominal
statistical uncertainty estimated for these next generation CMB experiments.
