When Teqûe was founded, a young guanaco was adopted due to the club was the youngest in the region by then.

The first years Teqüe played in the Club Chacras de Coria field.

The club has played matches against some of the most notable teams of Buenos Aires, such as SIC, San Cirano, Los Matreros.

Teqüe also disputed international games facing Bordeaux Etudiants, Vascos de Baigorri and Stade Français (France), Birkenhead Park FC, Dauntsey's School (England), Garda (Ireland), University of Edinburg (Scotland), Walcha (Australia), Universidad Católica, Universidad de Chile and Chile national team.

[3] In 2022, Teqüe won their first Torneo del Oeste championship after defeating Marista 26–24 in the final.