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According to MSDN, this function is already implemented:

' Code from MSDN
'
Dim myString As String = "ABCDE" 
Dim myChar As Char 
' The value of myChar is "D".
myChar = myString.Chars(3)

• Please indent your code.

• I would choose another, more meaningful name for your function: getCharAt or getByteFromString. It is now clear that the function operates on a string.

• I would use the clearer parameter name str instead of s.

• "Compress":

    place = place + 1
    getbyte = Mid(s, place, 1)
  
    ' change to
    getbyte = Mid(s, place + 1, 1)
  

  The first version is definitely not wrong or ugly, but why use an extra line if we could express the same logic in the same clear manner?

• You could use If to shorten your code:

    Private Function getbyte(str As String, ByVal place As Integer) As String
      getbyte = If(place < Len(str), Mid(str, place + 1, 1), "")
    End Function