The theory of phase noise caused by thermal fluctuations in an optical fiber is revised, accounting for both longitudinal and transverse phonons, and for the anisotropy of the elastooptic effect. A realistic optical mode field is accounted for. The theory is applied to calculations of bit error rates in DPSK coherent fiber-optic communication systems. Numerical results show that the thermal phase fluctuations are unimportant for transmission distances below 10000 km.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>