"Morality" is never decided by the individual. It is always a social construct representing an interval between what is desirable/acceptable and what is not desirable/not acceptable given certain circumstances. And it exists in a constant interplay between individual values and values perceived in the groups where he or she socializes (or is socialized).
Each group has its own rationale for legitimating values that, given enough time to mature, become institutionalized. This rationale may be contested within the group and from pressure from outside the group. But when some value becomes an institution, it is usually for the legitimization of a specific function for that group - either internally or in its relationship with other groups.
For instance, Max Weber shows how religious principles helped pave the way for capitalism. Protestant ethics stimulated people to work and accumulate wealth while living in austerity. Given the right conditions in 19th century Europe, this gave rise to specific "work ethics" that define many of today's "morals": like the idea of a professional "vocation", or simply that to be a useful member of society you need a "real job", something that you "do" outside your private setting.
So, "morality" doesn't ever depend only on what a given individual, or a specific group believes, but on the permanence of certain types of relationships among groups within one society. And it is continuously contested, just as relationships shift (or not). This brings other problems to the table, related to different entities in society having different levels of symbolic power that can be used to frame issues according to specific sets of values that suit them best. But that's a different debate.. Putting it in one sentence, morality is simply a form for the legitimation of social practices.
Anarchism isn't chaos. It doesn't mean "the rule of the fittest" in any way. Quite the contrary, it means that people recognize their interdependence in full. It means that you can self-organize with others and have the right for full political participation, while at the same time, recognizing those rights in everyone else. So "morals" in an anarchist society would hardly legitimize killing or stealing. Individualism is not egoism. You can have the first - in the sense that you can value each individual for him or herself, for his particular contribute and his own work and merit - without the second. Actually, the idea is that if you eliminate social inequality, no one will even need to steal.