  We experimentally observe many-body localization of interacting fermions in a
one-dimensional quasi-random optical lattice. We identify the many-body
localization transition through the relaxation dynamics of an
initially-prepared charge density wave. For sufficiently weak disorder the time
evolution appears ergodic and thermalizing, erasing all remnants of the initial
order. In contrast, above a critical disorder strength a significant portion of
the initial ordering persists, thereby serving as an effective order parameter
for localization. The stationary density wave order and the critical disorder
value show a distinctive dependence on the interaction strength, in agreement
with numerical simulations. We connect this dependence to the ubiquitous
logarithmic growth of entanglement entropy characterizing the generic many-body
localized phase.
