Writing to a text file

Hello,
I have the following  subroutine in an asp.net application class. The subroutine writes data to a text file upon application login.   My question is that if this function was called at the same time by two different  users would it cause any kind of error. Is there a need for a try catch?
 Public Shared Sub writeToLogFile(ByVal UserName  As String)
        Dim strLogMessage As String = String.Empty
        Dim strLogFile As String = System.Web.HttpContext.Current.Server.MapPath("~/Log.txt") Dim swLog As StreamWriter
        strLogMessage = DateTime.Now.ToShortDateString().ToString()  " ==> " & UserName
        If Not File.Exists(strLogFile) Then
        & ...