"with one condition" is grammatically correct and can be used in written English.
For example, "You can borrow my car with one condition—that you fill it up before returning it."
Mr. Harvey acquiesced, with one condition: "O.K., but I'm on the guest list when you play Madison Square Garden".
Despite the initial resistance, she managed to land a gig at a 150-person venue on Koh Samui that year, with one condition: "They said, 'You can play, but you will play for nobody' it was just the staff.
Chopra told Lee she was interested, with one condition: "I wanted to be cast as an actor on merit as being the best person for the job.
With one condition: "You better dress cool," he warned me.
"I was flattered," Mr. Wurst recalled, and agreed with one condition.
It came with one condition, that I train his amateur dance troupe.
We asked, and they accepted with only one condition: that the interview take place in Alaska.
A welcome to all people -- who they are and where they're at (with the one condition that they do not present an urgent danger to others).
He'd march into principals' offices himself with his one condition: that the classes be part of the curriculum, and not just an after-school activity.
Among the patients with CVDs, one condition was present in 290 (61.4%), two in 121 (25.6%) and three or more in 66 (14.0%) subjects.
At the end of the night, he told Aynaz she could live with him under one condition: She had to have sex with him whenever he wanted.
