We show analytically, numerically, and experimentally that a transversely s
table one-dimensional [(1 + 1)D] bright Kerr soliton can exist in a 3D bulk
medium. The transverse instability of the soliton is completely eliminated
if it is made sufficiently incoherent along the transverse dimension. We d
erive a criterion for the threshold of transverse instability that links th
e nonlinearity to the largest transverse correlation distance for which the
1D soliton is stable.