  The phase transition of Bose-Einstein condensation is studied in the critical
regime, when fluctuations extend far beyond the length scale of thermal de
Broglie waves. Using matter-wave interference we measure the correlation length
of these critical fluctuations as a function of temperature. The diverging
behavior of the correlation length above the critical temperature is observed,
from which we determine the critical exponent of the correlation length for a
trapped, weakly interacting Bose gas to be $\nu=0.67\pm 0.13$. This measurement
has direct implications for the understanding of second order phase
transitions.
