Trochu robustnejšie:

Private Sub Worksheet_Change(ByVal Target As Range)
    On Error GoTo ErrorHandler
    Application.EnableEvents = False
    
    Dim aRow As Range
    
    For Each aRow In Target.Rows
        aRow.EntireRow.Cells(1, 1).Value = Now
    Next
    
ErrorHandler:
    Application.EnableEvents = True
End Sub