Slice the eggs in half lengthwise. Remove the yolks and place them in a medium bowl or in the bowl of a food processor. Add the mayonnaise, mustard, and lemon juice. Mash or process until blended and smooth. Add the chives, salt, black pepper, and Tabasco and pulse just until combined. Taste for seasoning. Spoon the filling into the whites or pipe the filling using a pastry bag and tip. Refrigerate until ready to serve. Allow the stuffed eggs to set out at room temperature for 20 minutes before serving. Enjoy!