If utilitarianism is true, our morally permissible actions are constrained to the ones which maximize the net present value of total aggregate utility. Absent possibilities to reach the maximum by different actions, this means that, if we have chosen to act morally, we are not thereafter free to choose anything at all.
Free will is of course a debatable phenomenon. It is fine for reasonable people to disagree with me and claim that there is no such thing as free will - though I am probably right!). But whichever answer one reaches on the issue, it seems to be true that free will bestows upon us a certain dignity which we would otherwise lack.
Might not utilitarianism therefore rob us of that dignity? I am no utilitarian, but it seems to me that the answer is no. A utilitarian who is free to choose could simply keep making choices completely in accord with the utilitarian demands because that is what he fancies. Even if he believes utilitarianism is an objective moral fact, it will not stop him from arguing that a person can choose not to obey moral facts.
This reminds me of a classic attempt to refute free will. It starts by assuming that a person's actions are completely predictable (such as they are if a person always behaves according to strict utilitarianism), and notices that if actions are predictable the actor could not choose them. On the other hand, the attempt goes on, assume that actions are random and so unpredictable. In this case, the agent can hardly be said to choose, since choice would imply randomness. (But what if actions exhibit some tendencies with a measure of noise?)
What the attempt misses is that one could behave according to some rule because one wants to. This, incidentally, is also why rational choice is compatible with free will. Perhaps one simply wants to maximize one's own utility. That one wants it is no evidence for the proposition that one could not want differently.