  The recently discovered Parrondo's paradox claims that two losing games can
result, under random or periodic alternation of their dynamics, in a winning
game: "losing+losing=winning". In this paper we follow Parrondo's philosophy of
combining different dynamics and we apply it to the case of one-dimensional
quadratic maps. We prove that the periodic mixing of two chaotic dynamics
originates an ordered dynamics in certain cases. This provides an explicit
example (theoretically and numerically tested) of a different Parrondian
paradoxical phenomenon: "chaos+chaos=order"
