Packrat parsing is a popular technique for implementing top-down, unlimited-lookahead parsers that operate in guaranteed linear time. In this paper, we describe a method for turning a standard packrat parser into an incremental parser through a simple modification to its memoization strategy. By 'incremental', we mean that the parser can perform syntax analysis without completely reparsing the input after each edit operation. This makes packrat parsing suitable for interactive use in code editors and IDEs - even with large inputs. Our experiments show that with our technique, an incremental packrat parser for JavaScript can outperform even a hand-optimized, non-incremental parser.