Ed,

You might have to declare another variable to refer to a Text Stream object,
then include an additional line of code to open the file that way. Also, you
should use the AtEndOfStream property on the Text Stream object to prevent
running past the end of the file. Also, how do you plan to read multiple
lines of text file into a single Contents variable? Each line would probably
have to be added with a NewLine string (vbNewLine) (or vbCrLf) embedded
between it and the previous contents.

So your code (untested revision) might look like the following:

Dim FSO As Object, File As Object, Contents As String
Dim TS as Object
'Text Stream object.
Set FSO = CreateObject("Scripting.FileSystemObject")
Dim strFName As String
Dim strFPath As String
strFPath = ActiveWorkbook.Path & "\"
strFName = strFPath & "About.txt"

Set File = FSO.OpenTextFile(strFName)
Set TS = File.OpenAsTextStream(1, 0) 'Open the text file for reading in
ASCII format.

Contents = ""
Do While Not TS.AtEndOfStream
Contents = Contents & TS.ReadLine & vbNewLine
Loop

TS.Close

'Now do something with Contents.
--
Regards,
Bill