The three clubs have six points after two games this season with Caldas ahead on goal difference.
Caldas overcame a second-half red card to Patricio Perez to defeat Patriotas Boyaca 2-0 on Sunday and Chico trumped Alianza Petrolera 1-0.
On Saturday, Millonarios defeated La Equidad 1-0.
Caldas lead the Primera A with plus three goal difference, just ahead of Millonarios and Chico, who are both on plus two.
A first-half brace from Jose Heriberto Izquierdo saw Caldas beat Patriotas at the Estadio Palogrande, although the home side had to grind out the win after Perez was sent off in the 73rd minute.
In Tunja, Chico triumphed in front of their home fans thanks to Edwin Ernesto Avila's strike in first-half stoppage time.
Avila gave Alianza a shot at getting back into the match when he was red-carded in the 54th minute but the visitors were unable to capitalise, eventually having Felipe Aguilar sent off as well in stoppage time.
In the capital on Saturday, Millonarios triumphed in their derby at La Equidad's Estadio Metropolitano de Techo thanks to Fabian Vargas' 55th-minute goal.
Apertura champions Atletico Nacional were twice pegged back by Deportivo Cali as both clubs registered their first points of the new campaign with a 2-2 draw, while Santa Fe defeated Fortaleza 2-0.
In other results, Aguilas Doradas won 3-1 at Atletico Huila, Jorge Andres Aguirre struck twice as Junior defeated Uniautonoma 4-2 with Martin Enrique Arzuaga converting two penalties for the losers, while Envigado versus Deportes Tolima and Deportivo Pasto against Medellin both finished scoreless.
