It's crafty lefty reliever Steve Hamilton. Acquired in 1963 in return for Jim Coates, Steve remained a consistent performer out of the Yankee bullpen for the next 6-1/2 years until he was released in 1970.  His career stats with the Yankees include a 34-20 record, 2.78 ERA, allowing only 389 hits in 486 IP (311 appearances.)  He even started 7 games, completed two of them and hurled a 3-0 shutout on August 5th, 1966 in the nightcap of a double header against the Cleveland Indians. He saved 36 games with the Yankees, walked 150 and struck out 389 batters.

Of course, Steve was best known for his "Folly Floater" pitch.  A crowd pleaser that consisted of Steve stopping mid-delivery and tossing a high, soft lob over the plate. Most famously, he victimized Tony Horton of the Cleveland Indians who dared Hamilton to throw the pitch, determined to hit it out of the park.  The best he could manage was a foul pop-up with Thurman Munson making a sliding catch.  Defeated, Horton crawled back to the dugout on his hands and knees.

The image is from his 1966 Topps card (#503)

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Here's how other's had guessed:
Steve Hamilton - 422
Don Larsen - 30
Tommy Byrne - 22
Whitey Ford - 22
Bobby Shantz - 12
Jim Kaat - 18
Jim Coates - 17
Mel Stottlemyre - 14
Stan Bahnsen - 12
Fritz Peterson - 11
Lindy McDaniel - 10
Ralph Terry - 10
Dooley Womack - 10
Lefty Gomez - 8
Jim Bouton - 7
Allie Reynolds - 7
Spud Murray - 5
Bill Stafford - 5
Tom Sturdivant - 5
Art Ditmar - 4
Lou Gehrig - 4
Mickey Mantle - 4
Roger Maris - 4
Billy Martin - 4
Jack Aker - 3
Ewell Blackwell - 3
Clete Boyer - 3
Johnny Kucks - 3
Ed Lopat - 3
Bill Monboquette - 3
Joe Page - 3
Red Ruffing - 3
Bob Turley - 3
Jack Cullen - 2
Bob Grim - 2
Bob Kuzava - 2
Bob Lemon - 2
Phil Linz - 2
Don Mattingly - 2
Vic Raschi - 2
Hal Reniff - 2
Rugger Ardizoia - 1
Bill Bevens - 1
Bob Cerv - 1
Tex Clevenger - 1
Bud Daley - 1
Ryne Duren - 1
Doc Edwards - 1
Don Gullett - 1
Frank Howard - 1
Catfish Hunter - 1
Tommy John - 1
Mike Kekich - 1
Charlie Keller - 1
Al Leiter - 1
Duke Maas - 1
Mickey McDermott - 1
Gil McDougald - 1
Sam McDowell - 1
George McQuinn - 1
Joe Ostrowski - 1
Johnny Sain - 1
Norm Siebern - 1
Charlie Silvera - 1
Aaron Small - 1
Snuffy Stirnweiss - 1
Hal Stowe - 1
Ron Swoboda - 1
Fred Talbot - 1
Tom Tresh - 1
Steve Whitaker - 1
Gene Woodling - 1