Shape-averaged magnetoconductance (weak localization) is used for the
first time to obtain the electron phase coherence time tau(phi) in ope
n ballistic GaAs quantum dots. Values for tau(phi) in the range of tem
perature T from 0.34 to 4 K are found to be independent of dot area, a
nd are not consistent with the tau(phi) proportional to T-2 behavior e
xpected for isolated dots. Surprisingly, tau(phi)(T) agrees quantitati
vely with the predicted dephasing time for disordered two-dimensional
electron systems.