In time-resolved Faraday rotation experiments, we have detected an in-plane anisotropy of the electron spin-dephasing time (SDT) in an n-modulation-doped GaAs/Al0.3Ga0.7As single quantum well. The SDT was measured with magnetic fields of B <= 1 T, applied in the [110] and [1 (1) over bar0] in-plane crystal directions of the GaAs quantum well. For fields along [1 (1) over bar0], we have found up to a factor of about 2 larger SDT than in the perpendicular direction. The observed SDTs also show strong anisotropic magnetic-field dependence. Fully microscopic calculations, by numerically solving the kinetic spin Bloch equations considering the D'yakonov-Perel' and the Bir-Aronov-Pikus mechanisms, reproduce the experimental findings quantitatively. This quantitative analysis of the data allowed us to determine the relative strengths of Rashba and Dresselhaus terms in our sample. Moreover, we could predict the SDT for spins aligned in the [110] in-plane direction to be on the order of several nanoseconds, which is up to 2 orders of magnitude larger than that in the perpendicular in-plane direction.