I noticed that in the 2011 NIV, Job 28 is marked off as an interlude as does not appear in quotation marks; whereas in the 1984 NIV, the text appears in quotation marks and is considered a part of Job's final speech. I can see how 29:1 might recommend the 2011 approach. Should this passage about wisdom be considered an interlude by the narrator? If so, why might the narrator choose to place it there?
If you read the text straight through without the division into chapters, chapter 28 seems to flow naturally from the end of 27 -- the chapter division almost seems to be in the middle of a thought. I don't know why the chapters were divided the way they were, but they are not in the original text. Chapters 29-31 read clearly as one discourse. So I don't see clear textual support for it not being part of his discourse, though I can't prove it's not an authorial interruption.
One might argue that chapter 29 beginning with "Job continued..." means there must have been an interruption. I don't have an answer for that beyond noting that "X said... and X said" constructs appear elsewhere too. It's not common but it does happen.
Please note: This answer was written for a neutral, academic audience and is not intended to be interpreted in the context of a religious belief or doctrine.