Put the avocado cubes in a glass bowl. Add the cilantro, tomatoes, red onion, lime juice, jalapeno, cumin, salt and pepper. Gently, using 2 wooden spoons or paddles, work from the outside blending until the avocado cubes start to break up yet chunks still remain. Work slowly, taking time to ensure the guacamole stays chunky and creamy.
If not serving immediately, press a piece of plastic wrap directly on top of the guacamole to cover it completely so it doesn't brown. When ready to serve the guacamole, garnish with a tortilla chip in the middle of the bowl. Serve with the remaining chips on the side for dipping.