Chrome Extension Writing to Google Spreadsheet [closed]

Yes, it is definitely possible. I have used the Spreadsheet API extensively using Javascript. You’ll need to use the Protocol version of the API as documented here: https://developers.google.com/google-apps/spreadsheets/

This requires sending signed requests using OAuth2 (the older auth protocols aren’t really reliable anymore.) so I suggest using an OAuth2 library like JSO.
https://github.com/andreassolberg/jso

When writing your javascript you’ll need to write functions that create an XML string to interface with the Protocol API. Parsing the responses is pretty straight forward. I’ve included a snippet of the code I’ve used. You can also see my answer to a related question using JQuery here. JQuery .ajax POST to Spreadsheets API?

function appendSpreadsheet(){

 //Constructs the XML string to interface with the Spreadsheet API.
 //This function adds the value of the param foo to the cell in the first empty row in the column called 'columnTitle'. 
 //The Spreadsheet API will return an error if there isn't a column with that title.
 function constructAtomXML(foo){
  var atom = ["<?xml version='1.0' encoding='UTF-8'?>",
          '<entry xmlns="http://www.w3.org/2005/Atom" xmlns:gsx="http://schemas.google.com/spreadsheets/2006/extended">',//'--END_OF_PART\r\n',
          '<gsx:columnTitle>',foo,'</gsx:columnTitle>',//'--END_OF_PART\r\n',
          '</entry>'].join('');
  return atom;
 };

 var params = {
 'method': 'POST',
 'headers': {
   'GData-Version': '3.0',
   'Content-Type': 'application/atom+xml'
 },
 'body': constructAtomXML(foo)
 };

 var docId //Get this from the spreadsheet URL or from the Google Drive API.
 var worksheetId = 'od6'; //The worksheet Id for the first sheet is 'od6' by default.

 url="https://spreadsheets.google.com/feeds/list/"+docId+"https://stackoverflow.com/"+worksheetId+'/private/full';

 sendSignedRequest(url, handleSuccess, params); //Use your OAuth2 lib
}