Nicholas Kristof hosted the hangout, with five readers also asking questions
Hangouts are one of the features of Google+, the social network that launched 11 months ago, and allow people to participate in an online video conversation.
The New York Times hangout invited readers to nominate themselves to take part. Ten days before Thursday's hangout, columnist Nicholas Krystof, who moderated the interview, asked readers to help him "put her on the spot and challenge both of us with your questions".
Hundreds wanted to participate in the half-hour conversation, according to Kristof in the introduction to the video hangout.
Five participants were selected and ranged from a captain in the US Army speaking from Afghanistan, a high school pupil, a graduate student, an attorney and a physicist.
In the video introduction Kristof explains: "We are experimenting with using Google+ Hangout as a way of engaging with what we used to call readers, now you are viewers and part of the New York Times family in all kinds of ways."
It is not the first time the New York Times has hosted a Google+ Hangout, regularly experimenting as a way of allowing readers to engage with journalists.
Writing earlier this month, editorial page editor Andrew Rosenthal announced a series of hangouts on topics including: Room for Debate, "a forum for timely analysis and opinion on the news"; health and health policy; a "disunion" hangout, which will host a series of discussions on the civil war, and a hangout hosted by Op-Docs, "the opinion department's forum for short, opinionated documentaries".
Other news organisations have also embraced Google+ Hangouts, including Al Jazeera social media show The Stream, which regularly uses the format to allow viewers to take part and question interviewees during the live programme.