I'd actually use a combination of the techniques discussed here, using RedirectOutput() to eliminate the need to Open(), Write(), and Close() all the individual output files.
Code:
 
$SourceFile = 'file.csv'
$Counter = 1

Del 'c:\temp\subfile.????.csv'	; delete all output files


If $Open(5, $SourceFile, 2)	; open the source file
  $Line = ReadLine(5)		; read a line
  While Not @ERROR		; read until EndOfFile error
 
    ; create an index - 0000 to 9999 - to determine which group of 1000 we're in
    $Index = Right('0000' + CStr(Int($Counter / 1000)), 4)
 
    ; Define the output file based on a base file name/path, the index, and the extension
    $OutFile = 'c:\temp\subfile.' + $Index + '.csv'
 
    ; print the line, redirecting output to the current outfile
    $ = RedirectOutput($OutFile)
    $Line ?
    $ = RedirectOutput('')
 
    ; Read the next line and increment the counter
    $Line = ReadFile(5)
    $Counter = $Counter + 1
 
  Loop
 
  $ = Close(5)
 
Else
  ? 'Error opening ' $SourceFile ' - Aborting!' ? ?
  Exit 1
EndIf


Glenn

PS - this is an example - you'll want to add some error checking, and there's more efficient ways to handle the RedirectOutput. One thought - save the previous OutFile, and close/reopen the RedirectOutput only when it changes.
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Actually I am a Rocket Scientist! \:D