you've gotta qualify the Cells calls with a worksheet object too:
ThisWorkbook.Sheets(1).Range(ThisWorkbook.Sheets(1).Cells(1, 1), ThisWorkbook.Sheets(1).Cells(1, 3)).Value = _
BookA.Sheets(1).Range(BookA.Sheets(1).Cells(1, 1), BookA.Sheets(1).Cells(1, 3)).Value
for contiguous ranges like that you can also use Resize:
ThisWorkbook.Sheets(1).Cells(1, 1).Resize(, 3).Value = _
BookA.Sheets(1).Cells(1, 1).Resize(, 3).Value