  We present polarization measurements in the $2-8 \thinspace \mathrm{keV}$
band from blazar 1ES 0229+200, the first extreme high synchrotron peaked source
to be observed by the Imaging X-ray Polarimetry Explorer (IXPE). Combining two
exposures separated by about two weeks, we find the degree of polarization to
be $\Pi_{X} = 17.9 \pm 2.8 \%$ at an electric-vector position angle $\psi_X =
25.0 \pm 4.6^{\circ}$ using a spectropolarimetric fit from joint IXPE and
XMM-Newton observations. There is no evidence for the polarization degree or
angle varying significantly with energy or time on both short time scales
(hours) or longer time scales (days). The contemporaneous polarization degree
at optical wavelengths was $>$7$\times$ lower, making 1ES 0229+200 the most
strongly chromatic blazar yet observed. This high X-ray polarization compared
to the optical provides further support that X-ray emission in high-peaked
blazars originates in shock-accelerated, energy-stratified electron
populations, but is in tension with many recent modeling efforts attempting to
reproduce the spectral energy distribution of 1ES 0229+200 which attribute the
extremely high energy synchrotron and Compton peaks to Fermi acceleration in
the vicinity of strongly turbulent magnetic fields.
