  We study the polarized gluon distribution $\Delta g(x)$ in a longitudinally
polarized proton. We argue that the distribution can be calculated
approximately from the quark color currents found in simple quark models. The
first result from the MIT bag model as well as the non-relativistic quark model
shows that $\Delta g(x)$ is positive at all $x$. If this feature holds in QCD,
it imposes a strong constraint on phenomenological fits to experimental data.
The total gluon helicity $\Delta G$ from the bag model is about $0.3\hbar$ at
the scale of 1 GeV, considerably smaller than previous theoretical
expectations.
