Drain the 2 cups sliced pickled jalapenos and 1 cup dill pickle chips well and pat them dry with paper towels to remove excess liquid.
Place the drained jalapenos and pickle chips in a food processor. Add 1 tablespoon Tequila, 1 minced garlic clove, 1/4 cup chopped onion, 1 teaspoon chopped fresh dill, 1/2 teaspoon black pepper, and 1/4 teaspoon Tabasco sauce.
Pulse the mixture in short bursts until it is finely chopped but still has some texture, scraping down the sides once or twice as needed.
(Alternative, no food processor) Finely chop the drained jalapenos and pickle chips with a sharp knife, transfer them to a bowl, then add the Tequila, minced garlic, chopped onion, chopped fresh dill, black pepper, and Tabasco; mix until evenly combined.
Transfer the relish to a bowl or airtight container, cover, and chill for at least 1 hour before serving.