Here is the verse in additional context:
Ah! well a-day! what evil looks
Had I from old and young!
Instead of the cross, the albatross
About my neck was hung.
Why is the albatross there? Well, it is evidently taking place of "the cross". In the first two lines of this stanza, he speaks of how the people give him "evil looks", that is, disapproving ones. They do this, of course, because they killed the albatross. This was a maritime symbol of good luck. Now, since it has been slain, the mariner most likely willingly put the bird across his neck. I'm not so sure "chained" is the correct word. Whether or not is literal, I'd say, is besides the point. When reading poetry, you read not to read an account of what happened, but rather try to read into the meaning of the text.
Back to the bit about the cross. This text has evidently some type of Christian background. Not to say that it is a Christian poem; the two mentions of Christ's name, on lines 123 and 488 are not so much as invoking Christ as speaking his name. Now, let's take "the cross" to mean the Christian cross. This is a symbol of faith. To say that the slain albatross displaced the cross on his next (or as would be customary to be found on his neck) is most likely a statement about faith: that instead of having faith, the mariner "believes" for the lack of a better term, in luck. So perhaps this albatross could be said to be a statement of faith (rather, the lack thereof).
The quality of said albatross being dead, however, leaves something to think about...