Classic ASP, VBScript context.
A lot of articles including this Microsoft one, say you cannot use FileSystemObject to read Unicode files.
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Yes that documentation is out of date. The scripting component did go through a set of changes in its early days (some of them were breaking changes if you were using early binding) however since at least WK2000 SP4 and XP SP2 it has been very stable.
Just be careful what you mean by unicode. Sometimes the word unicode is used more broadly and can cover any encoding of unicode. FSO does not read for example UTF8 encodings of unicode. For that you would need to fall back on ADODB.Stream.