The following code retrieves the file called "log.txt", its contents are read using the FileReader API and appended to a new <textarea> on the page. If log.txt doesn't exist, an error is thrown.

GetFile.js

// Note: The file system has been prefixed as of Google Chrome 12:
window.requestFileSystem  = window.requestFileSystem || window.webkitRequestFileSystem;

function errorHandler(e) {
  var msg = '';

  switch (e.code) {
    case FileError.QUOTA_EXCEEDED_ERR:
      msg = 'QUOTA_EXCEEDED_ERR';
      break;
    case FileError.NOT_FOUND_ERR:
      msg = 'NOT_FOUND_ERR';
      break;
    case FileError.SECURITY_ERR:
      msg = 'SECURITY_ERR';
      break;
    case FileError.INVALID_MODIFICATION_ERR:
      msg = 'INVALID_MODIFICATION_ERR';
      break;
    case FileError.INVALID_STATE_ERR:
      msg = 'INVALID_STATE_ERR';
      break;
    default:
      msg = 'Unknown Error';
      break;
  };

  console.log('Error: ' + msg);
}


function onInitFs(fs) {

  fs.root.getFile('log.txt', {}, function(fileEntry) {

    // Get a File object representing the file,
    // then use FileReader to read its contents.
    fileEntry.file(function(file) {
       var reader = new FileReader();

       reader.onloadend = function(e) {
         var txtArea = document.createElement('textarea');
         txtArea.value = this.result;
         document.body.appendChild(txtArea);
       };

       reader.readAsText(file);
    }, errorHandler);

  }, errorHandler);

}

window.requestFileSystem(window.TEMPORARY, 1024*1024, onInitFs, errorHandler);