"one-on-one chat" is a perfectly correct and usable phrase in written English.
You can use it when referring to a conversation between two people, either in person or over the internet. For example, "The couple had a one-on-one chat about their plans for the future."
WASHINGTON — It took President Obama 18 months to invite the Senate Republican leader, Mitch McConnell, to the White House for a one-on-one chat.
The director made the attractive promise of a one-on-one chat to give feedback and career advice; a promise he never delivered on.
Internet inquiries come by e-mail (13,398 last year) and a one-on-one chat that resembles instant messaging (7,220 last year).
At the end of each panel, he gets each panellist to pick a few young people out of the audience to have a one-on-one chat after the panel.
That one-on-one chat quickly transformed into Francona holding clubhouse court for roughly a half-hour with a host of his former players including Dustin Pedroia, Clay Buchholz, Jarrod Saltalamacchia, Nick Punto and David Ortiz.
Connected2Me is a one-on-one chat service that connects registered profiles with anonymous site visitors.
They couldn't have housemates nipping into the bathroom and engaging in one-on-one chats.
Better, she says, to schedule one-on-one chats during walks between courses.
Rosie O'Donnell's new talk show, her first since 2002, is shown live and offers a mix of standup comedy, music, dance and one-on-one chats with celebrities about menopause creams and breast reduction.
The messaging app, which is available for Android and the iPhone, has similar features to most other messaging clients: stickers, emoji, the ability to draw on images like Snapchat and the choice of group or one-on-one chats.
Even during the 1988 strike, Mr. Walton, who teaches a class about law and the Hollywood guilds at Loyola Law School in Los Angeles, met frequently with Mr. Counter, sometimes in one-on-one chats that kept the sides engaged.
