Political map of South American nations 05 August 1865 (Paraguayan Offensives): When its war with Brazil began in December 1864, Paraguay swiftly overran southern Mato Grosso (Mato Grosso Campaign). However, to reach its Uruguayan allies, Paraguay needed to move through Argentina. When Argentina refused access, the Paraguayans invaded but were still too late to stop Brazil overthrowing the Uruguayan government (Uruguayan War). In May 1865, Brazil, Argentina, and Uruguay formed the Triple Alliance to defeat Paraguay (Treaty of the Triple Alliance).