I think it was when Frodo put the Ring on when he was escaping from Boromir and he climbed to the top of Anon Hen (sp?). He sees the Eye looking for him and hears in his mind take off the Ring!. At least that's as nearly as I can recall. I don't have Fellowship with me at the moment.
And suddenly he felt the Eye. There was an eye in the Dark Tower that did not sleep. He knew that it had become aware of his gaze. A fierce eager will was there. It leaped towards him; almost like a finger he felt it, searching for him. Very soon it would nail him down, know just exactly where he was. Amon Lhaw it touched. It glanced upon Tol Brandir he threw himself from the seat, crouching, covering his head with his grey hood.
He heard himself crying out: Never, never! Or was it: Verily I come, I come to you? He could not tell. Then as a flash from some other point of power there came to his mind another thought: Take it off! Take it off! Fool, take it off! Take off the Ring!
The two powers strove in him. For a moment, perfectly balanced between their piercing points, he writhed, tormented. Suddenly he was aware of himself again. Frodo, neither the Voice nor the Eye: free to choose, and with one remaining instant in which to do so. He took the Ring off his finger. He was kneeling in clear sunlight before the high seat. A black shadow seemed to pass like an arm above him; it missed Amon Hen and groped out west, and faded.
Then all the sky was clean and blue and birds sang in every tree. Frodo rose to his feet. A great weariness was on him, but his will was firm and his heart lighter. He spoke aloud to himself. `I will do now what I must,' he said. 'This at least is plain: the evil of the Ring is already at work even in the Company, and the Ring must leave them before it does more harm. I will go alone. Some I cannot trust, and those I can trust are too dear to me: poor old Sam, and Merry and Pippin. Strider, too: his heart yearns for Minas Tirith, and he will be needed there, now Boromir has fallen into evil. I will go alone. At once.'