Desktop software cannot be used on any sort of mobile device (like an IPad) or a Chromebook.  You need a full PC or Mac.

Are you trying to prepare a past year return?  2018 or earlier can only be prepared using desktop software.  If you need to prepare a 2019 return, you can use online TT on any device that can use the internet.  

You need a full Windows or Mac computer to install Turbo Tax.  You need to get a refund for the Desktop program then use the Online version.

Start an Online return here,

https://turbotax.intuit.com/personal-taxes/online/

If you used the Desktop program last year here’s How to transfer into the Online version, expand the blue link if you used the CD/download last year........

https://ttlc.intuit.com/community/entering-importing/help/how-do-i-transfer-last-year-s-return-into-...

If you used the Desktop program before you may not like the online version.  It has less features and no Forms Mode.  You can only do 1 return.  Your return is only saved online so be sure to save both the .tax2019 data file and the pdf file to your computer when you are done.  In case you need to amend in the future or if you need a copy to get a loan or something.  You might not be able to access your online return when you need a copy.

Can I process my taxes online using my chrome

Chrome what?  A ChromeBook or the browser Chrome?  If you don't have a full Windows or Mac computer you can  use the Online version here,  https://turbotax.intuit.com/personal-taxes/online/ 

Online version System Requirements
https://ttlc.intuit.com/community/system-requirements/help/turbotax-online-system-requirements/00/25...