The question in the title is silly, since few advocate complete equality. The question is better posed, "Is TOO MUCH inequality a problem?"
Of course, this begs the question in the other direction, since "too much" is by definition a problem. Can a society be so unequal that even a devotee of the "no initiation of force" principle would agree that state action, in the form of direct redistribution or indirect taxes and subsidies in kind would be justified?
I bring this up because there was a very well executed discussion in the NYT on essentially this question (though they don't credit the "no initiation of force" point, since the NYT even supported the initiation of force in Iraq).
My own thought: Two years ago I would have said that inequality, simply qua inequality, could never be a problem. The reason is that relative wealth is simply not an allowable argument in a utility function, and therefore the government is never justified to act. Allowing the inclusion of the individual's reaction to inequality as a justification for state action is simply to take the sin of envy and raise it to the status of an artificial virtue, "social justice."
I found Hayek's view on this persuasive. The problem is not RELATIVE wealth, but the absolute destitution of the very poorest. If, in absolute terms, the poorest members of a rich society are unable to provide for themselves and their families the basics of food, clothing, shelter, education, and health care, than state action might be considered. But to be clear: the problem is not that income is too unequal, but rather that the poorest are simply too poor. (One place I discussed this was in this paper, on pages 3 and 4).
But now... not so fast. I would admit that I may have been wrong, and in fact almost certainly was wrong. There are two conditions in which inequality is a problem per se, without resort to the absolute poverty claim.
1. The bargaining power of the least well off is small enough, compared to the bargaining power of the rest of society, to render economic exchange by the least well off not euvoluntary. Sweatshops may be a problem precisely because they really are the best opportunity for the very poor.
2. The political power of the very wealthy swamps the power of the population, and in particular disenfranchises the median voter, because the peculiar institutions of large democracies tilt power toward the "median dollar." This is the argument made by many, but perhaps most tenaciously by my good friend Tom Ferguson, in books such as this one, especially the appendix. (UPDATE: Daron A offers some interesting observations extending the interaction)
But even then, having admitted there is a problem, I expect I will differ about the solution. The solution to the first problem cannot be to cut off access to the market. Closing the sweatshop does nothing but make rich lefties feel better, and does nothing to help the abject workers.
And the solution to the second problem cannot be to confiscate wealth. The solution is to reduce the ambitions of government, and in consequence sharply circumscribe its powers. If it is true that government controls every aspect of our lives, from whom we marry to what we eat, than I agree that the very wealthy will have disproportionate influence over those decisions. But then the answer can't be to get rid of the very wealthy; instead, the answer is get rid of the government controls.