You are able to export your account history from the Adobe Air version to the Chrome app. We strongly recommend you to migrate to SocialBro for Chrome, if you use a free version of our tool, because of a bug from Adobe Air.
To do this, click on the Settings icon in the top navigation bar.
Choose the Account tab and click on Export History.
Then, in the Chrome app, click on the Settings icon again, and click on Import History, after selecting the exported file.
Please make sure that you have the latest version of Google Chrome.