A long chain of command certainly does have advantages and disadvantages. Let's go over the most extreme example, the military. A military organization has a general at the top and at the bottom is a private. It is the best example there is, I think, of a long chain of command.
A few advantages come quickly to mind. One advantage to this is that the span of control is not too wide. The general does not have to give direct orders to tens of thousands of privates at the bottom, just to the lieutenant general beneath him or her and so on down the line until a lieutenant or captain gets the orders, transmits them to a sergeant, who then tells the troops what to do. Each person is responsible for a smaller number of people, which makes for much better management and control. Another advantage is that the person at the top in such an organization is able to have a clear mind to think about the big picture, and strategize about what troops to deploy where, or how to eliminate the culture of sexual harassment. At each level in a long chain of command, the responsibilities are delineated in a way that affords the person responsible the time and energy to focus on just those delineated responsibilities. The Major does not worry about whether the cook is doing a good job or how many medics are attached to a particular unit. Someone below him or her has this concern. Another advantage is in the way communication works. Privates who have complaints or suggestions do not call the general with them. They go through the chain of command. This reduces the "clutter" at the top and is meant to ensure that the person at the top does not use all of his or her time putting out small fires, not the best use of time for a general. In the military, at least, this very long chain of command seems to instill discipline in the ranks quite effectively, perhaps because of the span of control and the communications mechanisms.
Disadvantages there certainly are, though. There is almost a complete lack of autonomy at the lower levels, so that decision-making is seldom localized. This means that the people on the spot, closest to the facts, are usually unable to act. They must await disposition from a higher level, which means that the best decisions are not always being made. Another disadvantage is in the long line of communication. There probably are some times that it would be good for a private to tell a general something, and this chain of command makes that a virtual impossibility. Another disadvantage is that the people at the top can feel so removed from the people below that the people below are not as motivated as they could be. Most people like to know whom they are working for, I think, and to see that person at least occasionally. This is why generals do go around talking to troops, but it is unlikely that they ever get around often enough to really motivate people.
These advantages and disadvantages exist just as much in civilian organizations as they do in the military, and if you think about a very large company, you will be able to see their application easily.