To have a perfect batting average of 1.000, you have to have very few at-bats. The record for most at bats while maintaining a 1.000 batting average is three, held by John Paciorek. No player has come up to bat four times or more and gotten a hit every time. There are very few positive records a hitter can hold by virtue of not being good enough to get to do it very often.
Three Yankees have a career batting average of 1.000. Five players have hit 1.000 in their Yankee careers, but two got at-bats in other places. In these three players' cases, for various reasons, they were given one at-bat, got a hit, and have never been asked to step into the batter's box again.
The most recent player got his one hit just last season. Yankees reliever and perpetual Scranton-to-New York bus passenger Branden Pinder is one of these players. Pinder was brought in to finish off a blowout win over the Braves in Atlanta on August 30th. The Yankees were up 17-6 going into the inning and batted around to Pinder's spot in the lineup, tacking on another run in the process. Not wanting to use a pinch hitter up 12 runs, the Yankees let Pinder hit. This happened:
Pinder still has time to get another at-bat in his career. However, he is a relief pitcher on an AL team, so the odds aren't in his favor, at least for the foreseeable future.
In 1972, another Yankees pitcher accomplished the feat. A fourth round pick of the Yankees in 1967, Larry Gowell, made his major league debut out of the bullpen on September 21, 1972. Two weeks later on October 4th, he was the starting pitcher as the Yankees took on the Brewers. Gowell led off the bottom of the third with a double. When he was due up for his second at-bat, he was replaced by pinch hitter Frank Tepedino, who grounded into a force out. They should have let Gowell hit again. The Yankees lost the game 1-0 and Gowell had one of just three Yankees' hits. Gowell played two more seasons in the Yankees' system, but never made it back to the big leagues. The designated hitter was then implemented for the 1973 season.
The final player to do this is the delightfully named Heinie Odom, and he was actually a position player. Late in a 10-1 loss to the Washington Senators, he was sent up as a pinch hitter for Joe Dugan. He picked up a single and never played in the majors again.
The longest major league tenure of any player on this list is Pinder and he's only played 25 games. Despite perfection, neither Gowell or Odom ever batted again. Baseball is cruel sometimes.
All date courtesy of the Baseball-Reference Play Index