[olbeup]

Perdón, faltan las comillas del final de la sql:

Código Delphi [-]
procedure TForm1.Button1Click(Sender: TObject);
begin
  if ADOConnection1.Connected then
    ADOConnection1.Close;

  with ADOQuery1 do
  begin
    SQL.Clear;

    SQL.Add('SELECT');
    SQL.Add('    MAX(FECHA) AS ULTIMAFECHA');
    SQL.Add('  FROM Personas');
    SQL.Add('  WHERE PERSONAS_ID = 1');

    Open;
  end;

  with ADOQuery1.DataSource.DataSet do
    if FieldByName('ULTIMAFECHA').IsNull then
      DateTimePicker1.Date := now
    else
      DateTimePicker1.Date := FieldByName('ULTIMAFECHA').AsDateTime;
end;

Un saludo