  We present ALMA 97.5 GHz total intensity and linear polarization observations
of the mm-band afterglow of GRB 190114C spanning 2.2 to 5.2 hours after the
burst. We detect linear polarization at the $\approx 5\,\sigma$ level,
decreasing from $\Pi=(0.87\pm0.13)\%$ to $(0.60\pm0.19)\%$, and evolving in
polarization position angle from $(10\pm5)^\circ$ to $(-44\pm12)^\circ$ during
the course of the observations. This represents the first detection of
polarized millimeter emission in a $\gamma$-ray burst. We show that the optical
and X-ray observations between $0.03$ days and $\sim0.3$ days are consistent
with a fast cooling forward shock expanding into a wind environment. However,
the optical observations at $\lesssim0.03$ days, as well as the radio and
millimeter observations arise from a separate component, which we interpret as
emission from the reverse-shocked ejecta. Using the measured linear
polarization, we constrain the coherence scale of tangled magnetic fields in
the ejecta to an angular size of $\theta_{\rm B} \approx10^{-3}$ radian, while
the rotation of the polarization angle rules out the presence of large scale,
ordered axisymmetric magnetic fields, and in particular a large scale toroidal
field, in the jet.
