This is very poetic language, and I think it helps to give this verse the context of the two preceding it:
You shall be free indeed when your days are not without a care nor your nights without a want and a grief,
But rather when these things girdle your life and yet you rise above them naked and unbound.
And how shall you rise beyond your days and nights unless you break the chains which you at the dawn of your understanding have fastened around your noon hour?
In this context, the writer is referring to people's ability to rise beyond their cares and wants, day and night.
Because the writer then goes on to talk about this as rising 'beyond your days and nights', I think the writer is using 'noon hour' as a metaphor for 'waist', or something central. So the 'noon hour' is describing the notion of the 'central psyche' of the people to whom the writer is referring, around which they have fastened 'chains' which need to be broken.
The suggestion that the references to 'noon hour' and 'chains' are metaphorical rather than literal is strongly reenforced in the following verse, which states that 'freedom is the strongest of these chains'.