Rebuild Index on SQL 2000 Database fails due to duplicate key found - how to resolve?

I have a SQL 2000 database that is throwing a lot of errors after a checkdb. I've attempted to run a CHECKDB Repair_Rebuild which failed. Here are the first 30 or so lines of the log:

Server: Msg 1505, Level 16, State 1, Line 1
CREATE UNIQUE INDEX terminated because a duplicate key was found for index ID 1. Most significant primary key is '95556616'.
Server: Msg 8978, Level 16, State 1, Line 1
Table error: Object ID 741577680, index ID 1. Page (1:15544819) is missing a reference from previous page (1:15544816). Possible chain linkage problem.
Server: Msg 8935, Level 16, State 1, Line 1
Table error: Object ID 741577680, index ID 1. The previous link (1:6231350) on page (1:15774924) does not match the previous page (1:15776528) that the parent (1:9225193), slot 71 expects for this page.
Server: Msg 8937, Level 16, State 1, Line 1
Table error: Object ID 741577680, index ID 1. B-tree page (1:15774924) has two parent nodes (0:1), slot 0 and (4:4173), slot 4.
Server: Msg 8937, Level 16, State 1, Line 1
Table error: Object ID 741577680, index ID 1. B-tree page (1:15774925) has two parent nodes (1:9540125), slot 98 and (1:9225193), slot 1.
Server: Msg 8937, Level 16, State 1, Line 1
Table error: Object ID 741577680, index ID 1. B-tree page (1:15774926) has two parent nodes (1:9540125), slot 97 and (1:9225193), slot 1.
Server: Msg 8937, Level 16, State 1, Line 1
Table error: Object ID 741577680, index ID 1. B-tree page (1:15774927) has two parent nodes (1:9540125), slot 101 and (1:9225193), slot 1.
Server: Msg 8978, Level 16, State 1, Line 1
Table error: Object ID 741577680, index ID 1. Page (1:15776528) is missing a reference from previous page (1:15774925). Possible chain linkage problem.
DBCC results for 'MyTable'.
        Repairing this error requires other errors to be corrected first.
        Repairing this error requires other errors to be corrected first.
        Repairing this error requires other errors to be corrected first.
        Repairing this error requires other errors to be corrected first.
        Repairing this error requires other errors to be corrected first.
        Repairing this error requires other errors to be corrected first.


I don't understand how it's possible that a unique index can have duplicate keys - shouldn't SQL have refused the insert since it wasn't unique?

How can I get this index rebuilt?
KThraceAsked:
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ste5anSenior DeveloperCommented:
Nope, due the problems reported by CHECKDB, data corruption has occured. Thus the only way is to rebuild this table.
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KThraceAuthor Commented:
Understood. Which involves exporting the data, recreating the table, and then importing the data.

Am I not then going to run into problems with the non unique values? I still don't understand how duplicate keys got into the table...
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ste5anSenior DeveloperCommented:
The corruption may have affected the primary key. Thus bypassing the uniqueness check. Anorher possible reason: the corruption created the duplicate valuė.
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