  We present the results of a full QCD lattice calculation of the flavor
singlet axial vector coupling $G_A^1$ of the proton. The simulation has been
carried out on a $16^3\times 32$ lattice at $\beta=5.6$ with $n_f=2$ dynamical
Wilson fermions. It turns out that the statistical quality of the connected
contribution to $G_A^1$ is excellent, whereas the disconnected part is
accessible but suffers from large statistical fluctuations. Using a 1st order
tadpole improved renormalization constant $Z_A$, we estimate $G_A^1 =
0.20(12)$.
