Add a unique key field to view without redefining table

We have a table with millions of records and has no unique key defined, and
no data exists in it for which a unique key could be defined.
Historically, it has been ONLY a write and read only file; no updates or
deletes. The exception is that, sometimes, one of the developers will need
to manually update a record.

We have a new requirement to send inserts, updates, and deletes of several
files to another system. With this new requirement, we now need to
uniquely identify all records in this file with no unique keys. We are
trying to avoid changing the definition of the physical file or its
logicals, since there are 600 programs that use it.

So, I am wondering if it is possible to create a view that "attaches" some
kind of unique key value that the system manages. I seem to vaguely recall
that SQL provides some mechanism to do this, but my search failed either
because I am wrong or I am using the wrong search terms.

If this sounds workable, I just need the right terms to search and RTFM and
find online articles.

TIA,
- Dan