  If a single line of sight (LOS) intercepts multiple dust clouds of different
spectral energy distributions and magnetic field orientations, the frequency
scaling of each of the Stokes $Q$ and $U$ parameters of thermal dust emission
may be different ("LOS frequency decorrelation"). We present first evidence for
LOS frequency decorrelation in $Planck$ data. We use independent,
neutral-hydrogen--measurements of the number of clouds per LOS and the magnetic
field orientation in each cloud to select two sets of sightlines: (i) a target
sample (pixels likely to exhibit LOS frequency decorrelation); (ii) a control
sample (pixels lacking complex LOS structure). We test the null hypothesis that
LOS frequency decorrelation is not detectable in $Planck$ 353 and 217~GHz
polarization data at high Galactic latitudes. The data reject this hypothesis
at high significance. The detection is robust against choice of CMB map and
map-making pipeline. The observed change in polarization angle due to LOS
frequency decorrelation is detectable above the $Planck$ noise level. The
probability that the detected effect is due to noise alone ranges from $5\times
10^{-2}$ to $4\times 10^{-7}$, depending on the CMB subtraction algorithm and
treatment of residual systematics; correcting for residual systematics
increases the significance of the effect. The LOS decorrelation effect is
stronger for sightlines with more misaligned magnetic fields, as expected. We
estimate that an intrinsic variation of $\sim15\%$ in the ratio of 353 to
217~GHz polarized emission between clouds is sufficient to reproduce the
measured effect. Our finding underlines the importance of ongoing studies to
map the 3D structure of the magnetized dusty ISM that could help component
separation methods to account for frequency decorrelation effects in CMB
polarization studies.
