Voyager IRIS observations have revealed that the Jovian para-hydrogen fraction is not in thermodynamic equilibrium near the NH3 cloud top. This implies that a vertical gradient exists between the high-temperature equilibrium value of 0.25 at depth and the cloud top values measured by Voyager. We use an anisotropic multiple-scattering radiative transfer model to retrieve the height-dependent para-hydrogen profile. While the centers of the S(0) and S(1) hydrogen lines originate near the tropopause (i.e., above the NH3 cloud top), emission in the wing of the S(0) line originates within the NH3 cloud layer. The inclusion of spectrally dependent multiple-scattering calculations allows us to use the variation in gaseous absorption strength from the line center to the wing to retrieve the height-dependent para-fraction profile. We find that a vertical correlation exists between the location of the para-hydrogen gradient and the NH3 cloud, strongly suggesting that paramagnetic conversion on NH3 cloud particle surfaces is the dominant equilibration mechanism. Below the NH3 cloud layer, the para fraction is constant with depth and equal to the high-temperature equilibrium value of 0.25. The degree of cloud-top equilibration appears to depend on the optical depth of the NH3 cloud layer. Belt-zone differences exist in the degree of equilibration. Larger, more nearly equilibrated para-fraction values are found in zones. Belt-zone differences in the strength of the para-hydrogen gradient also exist. In belts, the gradient is clearly associated with the location of the NH3 cloud, and equilibration begins at cloud base, almost-equal-to 0.5-0.55 bar. In zones, "equilibration" does not begin until 0.4 bar, roughly 0.1 bar above the NH3 cloud base. This difference is most likely a consequence of the advection of low para-fraction values from depth.