For the filling: Mix together the chicken, cilantro, mayonnaise, salt, pepper to taste, the avocados and lime juice. Cover and refrigerate. For the dough: Mix together the water and salt in a large bowl, and then slowly add the cornmeal as you mix with your fingers. Mix and knead until it forms a soft dough. When you can pick up all of the dough in one mass, it's ready to form the arepas. Divide the dough into 8 balls, then gently flatten and form into discs.
Heat a lightly-oiled griddle or nonstick skillet over high heat. Preheat a grill to medium heat.
Cook the arepas on the griddle until they release from the cooking surface and are able to be moved, about 1 minute 30 seconds, and then flip and cook the other side for another 1 minute 30 seconds. Transfer the arepas to the grill and grill until lightly browned in spots, about 5 minutes per side. The arepas are ready when they sound like a drum when tapped.
Split the arepas in half, then scrape out and discard some of the middle. Stuff the arepas with the chicken mixture and eat while still piping hot.
Recipe courtesy of Eunice Marcano, Antojitos mi Colombia Bakery, Charlotte, NC