Aria-live attribute not working on chrome

Edit: December 2020 This answer is not so accurate anymore. Chrome has made some great strides in improving accessibility and this answer is likely not relevant if you are still experiencing this problem. I would suggest looking into some of the aria-live specs to better understand how it should be used, as most issues with it not being announced are likely due to things that can be fixed in the implementation rather than an NVDA+Chrome issue.

Original Answer:

Chrome is not commonly used by screenreaders and is lacking in some key accessibility areas. NVDA is most commonly used with Firefox as it's the one of the best browser-screenreader pairings.

This resource from a leading accessibility firm doesn't list chrome as supporting it (although Chrome is significantly far behind in terms of adoption by users with assistive technology - they aren't even mentioned on the page): https://www.paciellogroup.com/blog/2014/03/screen-reader-support-aria-live-regions/

If you're interested in common browser pairings (eg. which screenreader/browser combinations are worth supporting to accommodate the majority of users), please keep an eye on the webaim screenreader surveys - they're the best resource I've come across for statistics.http://webaim.org/projects/screenreadersurvey6/

apologies for not being able to directly answer why Chrome doesn't seem to work well with NVDA - It's a dangerous road to go down as there are numerous areas where they don't work well together. Considering the usage of Chrome/NVDA users it might not be worth it.