Heat a heavy-bottomed pot over medium-high heat with the EVOO. Cook onions, garlic, and jalapeño until soft, about 4 minutes.
Add chili powder and cumin, and cook for another minute. Add the tomatillo salsa, beer and stock. Bring up to a bubble and add in the shredded chicken. Simmer for 10-15 minutes.
Meanwhile, grind 2 handfuls of the tortilla chips and the cilantro leaves in a food processor. Add this mixture to the chili and continue cooking until it thickens, about 8-10 minutes.
Right before spooning into bowls, add in the lime juice and serve with some whole corn tortilla chips alongside.