The Mexican club, who are present by virtue of their runner-up finish in the 2013 Clausura, remain the joint-most successful club in the history of North America's premier cup competition.
But they have not tasted success in the tournament since 1997, and will be keen to get off to a good start when they host the reigning Costa Rican champions - who beat Valencia 6-1 in their first game.
Another Mexican side, two-time champions Toluca, are also in action on Thursday, as they travel to take on Comunicaciones of Guatemala at Estadio Cementos Progreso hoping to follow up their 3-1 win over Caledonia AIA.
Two American teams will get their campaigns under way in the latest round of fixtures, with LA Galaxy taking on Cartagines at the Stubhub Center, while Houston Dynamo face W Connection in Trinidad and Tobago.
The other Major League Soccer representatives have been drawn together in Group 5, but San Jose Earthquakes will be unable to bounce back from their defeat to Montreal Impact as they sit out while the Canadian side face Heredia of Guatemala.
Elsewhere, Sporting San Miguelito of Panama and Nicaragua's Real Esteli need to recover from losing their first matches when they face Alajuelense and Olimpia respectively.
And Olimpia's fellow Hondurans Victoria meet Tijuana of Mexico at Estadio Municipal Celibeno Nilmo.