  Magnetoelectric effects in the chiral magnet CsCuCl$_3$ have been
investigated through the magnetization and electric polarization measurements
in pulsed high magnetic fields. If the magnetic field is applied normal to the
spin chiral c-axis, a plateau and a jump in magnetization are observed. Between
the plateau and the jump in magnetization, a small but significant electric
polarization of about 0.25 {\mu}C/m$^2$ along the a-axis is observed with the
field applied almost perpendicular to the ac-plane. In addition, the
paramagnetoelectric effect expected from the point group symmetry is confirmed.
The emergence of the electric polarization is explained by the cooperation of
the local electric polarization on the chiral solitonic spin arrangement and
the paramagnetoelectric effect. Hence, we interpret this novel multiferroic
phase in CsCuCl$_3$ as a polar solitonic phase.
