  We study the effect of a close encounter of a passing star on the shape of
the inner Oort Cloud, using the impulse approximation. The deviation of the
perturbed Oort Cloud from sphericity adds angular fluctuations to the
brightness of the Cosmic Microwave Background (CMB) due to thermal emission by
the comets. An encounter with a solar-mass star at an impact parameter of $1750
\au$, as expected based on the abundance and velocity dispersion of stars in
the solar neighborhood, leads to a quadrupole moment in the square of the
fractional CMB intensity fluctuation of $C_2 = 4.5 \times 10^{-15}, 6.7 \times
10^{-12}, 1.1 \times 10^{-9}$ at $\nu = 30, 353, 545 \GHz$ (these being the
frequency bands of the upcoming Planck satellite). We also quantify the
quadrupole spectral distortions produced by the Scattered Disc, which will
exist regardless of any perturbation and the subsequent shape of the Oort
Cloud. For comparison, the square fractional temperature fluctuation quadrupole
moment predicted by the current cosmological model is $C_2 = 1.76 \times
10^{-10}$, which corresponds to fluctuations in the CMB intensity of $C_2 = 2.9
\times 10^{-10}, 6.8 \times 10^{-9}, 1.6 \times 10^{-8}$ at $\nu = 30, 353, 545
\GHz$. Finally, we discuss how a measurement of the anisotropic spectral
distortions could be used to constrain the trajectory of the closest stellar
fly-by.
