The 33 year old, who came through qualifying at Walton Heath to earn a spot at Pebble Beach, moved to level par, six behind leader Dustin Johnson with a round to go.
"I had tried to qualify many times for this Open and the British Open and this is the first time I made it at Walton Heath," said the three-time European Tour winner.
"It's great to be in this position after three rounds, a fantastic feeling. We get links courses for the Dunhill Links but this is the one US Open I am glad to play. My putting was very good form nine or ten feet.
Havret revealed how special it was to secure his starting spot at the famous California venue.
"Something I always wanted to do - to play these Opens," he added. "I've felt that for the last 25 years. The four Majors are something else and I want to be there and I want to win.
"Tomorrow? My thoughts are the same for every tournament. When I won my first event in Italy I felt I could win and the two I won in Scotland. Especially Loch Lomond played in the last group with Phil (Mickelson) and beat him in a play-off so I know that anything is possible.
"If you had said that when I was 15 years old I wouldn't have believed it but it's happening and it's why I work so hard.
"Maybe I can play the final round at Pebble Beach with Tiger Woods. I've never played with him. I hope I don't think too much about it. We'll see.
"It's a very important day and I will take it as it comes and if I putt as well, then that's good. If I have to fight for top ten then I will fight. I played in the last group in the Deutsche Bank in 2004 and shot 82. I was leading by two and was in the final group with Padraig Harrington and finished 25th.
"I know anything can happen in golf so I will just focus on my game and see what happens."