A member of the LPGA Tour since 2012, Martin has not yet won at that level but has victories on the Symetra Tour to her credit.
Martin utilised her great strength of accuracy from the tee to compiled a second consecutive round of 69 to edge three shots clear of So Yeon Ryu and Spain's Beatriz Recari with Sun Jun Ahn and Julietta Granada one shot further back.
Martin is clearly a very strategic player not blessed with a power game but one that is built around plotting her way around the golf course.
"I definitely have a game plan every single tournament. So that's something specific I do. That's something I focus very much on, and I've had three wins on the FUTURES Tour, which is now the Symetra Tour.
"I said earlier that a win is a win, and I think of course a major is absolutely more of a challenge and there is a lot more on the line here, but I mean, when I started playing golf, I mean, there's some things you pick out your strategy and then you work on executing that to the best of your ability. And I think any golf course you go to in any tournament, that's the objective, and whoever does that the best is going to win at the end of the week."
Ryu is shaping as a genuine chance to add a British Open title to the US Open she won earlier in her career. She has played this event well in the past and has been in good form this season in the US.
"You know, the U.S. Open and British is quite different," said Ryu. "That's why I like links golf courses, we have so many options. We can hit 5 wood and we can hit driver and also we can hit 5 iron at the same teeing ground.
"So I think that's why I really like links golf course and I think that's why I want to win the British Open, and in that case, I can hold the U.S. Open trophy and the British Open trophy and it will be awesome."
Only nine players have broken par and with an inexperienced Martin a three shot leader a lot of players even over par will still fancy their chances over the closing 36 holes including the world number one Stacy Lewis who is at 1 over and seven from the lead.
Lewis is aware however that her game will need to improve sharply if she is to defend her title.
"It was about as up and down as you could get, said Lewis after her second round of 74. "It was all over the place today. I hit some really good shots and hit some pretty poor shots, too. You know, my short game just didn't really help me out today.
"So got to shore that up for the weekend but I'm still in this thing. This golf course is playing so hard and just got to keep hanging around and hopefully I can shoot a good number tomorrow."
Lydia Ko leads a disappointing Australasian challenge, the 17 year old New Zealander in 34th position, Sarah Kemp and Nikki Campbell 49th after Kemp struggled following a good start to the event.
Three time winner Karrie Webb missed the cut after announcing earlier in the week she had split with long time coach Ian Triggs.