In Chapter III, Mill addresses the question of the sanction of moral obligation with respect to utility. The matter at hand is that moral values seem by definition to impute within us a charge to carry them out; it is this prescriptivity for which Mill feels moral theories, including his own, must account.
The structure of Mill's argument in responding to this question consists of the place of origin of prescriptivity relative to the moral agent. Thus, he stipulates that there exist origins of duty both internal and external to the agent. Logically, by considering both he ostensibly covers the scope of possibilities in terms of precisely where the duty originated.
The first class of duty origin, with which Mill is less concerned, is external sources. Mill claims in essence that we have no reason to believe that utilitarianism would not be privileged to the same external sources of sanction that other theories have been purported to have - namely, divine sanction. Mill also adds that insofar as the interests of other humans with whom we coexist can constitute external sanction, we have reason to believe the utilitarianism would be sanctioned more than any other moral system.
Mill is more interested in addressing internal sources of sanction for utilitarianism. The major internal sanction that Mill denotes is the conscience. Though extant in our common vernacular and of a similar meaning to Mill, it is worth noting that he is particularly interested in the aspect of consciousness that constitutes an internal censor of breaking perceived moral duties.
In effect, Mill's appeal to consciousness is that people subjectively intuit the sanction of utility. The reader ought to draw a parallel with Mill's conception of moral proof, because the conscience is precisely the arbiter of the standard of proof that Mill has in mind. It is perhaps reductive to call this faculty "moral intuition"; more correctly, Mill is referring to the faculty of our reason by which we perceive moral duties and are able to analyze them rigorously.
Mill acknowledges that there exists a concern, particularly in discourses of sanction, of whether internal sanction is implanted by the moral status of the external world, or if it is innate. Suffice it to say that Mill does not see this question as having any bearing on his argument. The reasoning behind this is that an innate ontology would very reasonably fit with a system based around pleasure and pain, whereas an implanted system would reflect the previously-mentioned force of the interests of others.
Further considering the interests of others, Mill makes a final point that the sanction of utility also comes from more fundamental human sentiments, as he believes all moral theory must. The sentiments Mill has in mind are our social sentiments: in particular, we desire unity and harmony amongst ourselves and other beings. A moral system based on maximizing happiness and minimizing unhappiness in the group is an ideal means to that end.
Note that this is virtually the only place where God significantly enters Mill's argument. As with animal considerations discussed in Chapter II, this is probably a relic of Mill's time. As devoutness was the norm, it was typical for morality to derive its sanction directly from God; it was no doubt important for Mill to point out that there was no reason to suppose that God would not impart utilitarianism on people as much as any other theory.
Also note the relatively small amount of space devoted here to mentioning God. Mill's emphasis is clearly on democratizing ethics, and that comes out plainly in his focus regarding external sanction on the interests of other people. The idea is that the very act of living in society sanctions morality and, specifically, utility more than the divine would.
This social focus is driven home by the corroboration of conscience with what Mill calls our social sentiments. Mill evidently believes that, whether internally or externally sanctioned, it is the basic fabric of society that ultimately supports utilitarianism's ontology.
This leads to the question of what would happen if someone were raised outside of society. Suppose a baby is left to grow up alone on an island and then is transplanted to a city. Would he be able to behave morally?
One answer is to question whether any such person would survive in the first place. What Mill has grasped is that society on some level seems necessary to our very existence; as such, it is difficult to even model what sort of person would exist, morally or not, outside its bounds.