  A wide range of quasi-one-dimensional materials, consisting of weakly coupled
chains, undergo three-dimensional phase transitions that can be described by a
complex order parameter. A Ginzburg-Landau theory is derived for such a
transition. It is shown that intrachain fluctuations in the order parameter
play a crucial role and must be treated exactly. The effect of these
fluctuations is determined by a single dimensionless parameter. The
three-dimensional transition temperature, the associated specific heat jump,
coherence lengths, and width of the critical region, are computed assuming that
the single chain Ginzburg-Landau coefficients are independent of temperature.
The width of the critical region, estimated from the Ginzburg criterion, is
virtually parameter independent, being about 5-8 per cent of the transition
temperature. To appear in {\it Physical Review B,} March 1, 1995.
