var
  filename: string;
  sr: TStreamReader;
  sl: TStringList;
  total, blocksize: integer;
begin
  filename := 'thefilenamegoeshere';
  sl := TStringList.Create;
  sr := TStreamReader.Create(filename, true);
  sl.Capacity := sr.BaseStream.Size div 100;
  total := 0; // Total number of lines in the file (after it is read in)
  blocksize := 10000; // The number of lines per "block"
  try
    sl.BeginUpdate;
    try
      while not sr.EndOfStream do
        begin
          sl.Clear;
          while not (sl.Count >= blocksize) do
            begin
              sl.Add(sr.ReadLine);
              total := total + 1;
              if (sr.EndOfStream = true) then break;
            end;
          // Handle the current block of lines here
        end;
    finally
      sl.EndUpdate;
    end;
  finally
    sr.Free;
    sl.Free;
  end;
end;