Harry, or 'H' as his friends nicknamed him, came to Milltown in September 1978, one year after Johnny Giles had been appointed player/manager. He was a number of full-time players who Giles signed up as part of the policy to develop a full-time professional set up at Milltown. Other players who were involved in the scheme at the time were Pierce O'Leary, Alan Campbell and Ritchie Bayly.
Harry made his Rovers debut on the 20th of December 1978 in a Leinster Senior Cup quarter final win against Dunleary Celtic at Tolka Park. His league debut came on the 3rd of April 1979 in a 4-0 win against Cork Celtic at Milltown. Along the way to senior status Harry picked up a few honours. He was capped for the Irish schoolboys at U15, U17 and youths level.
In his only his second full season at Milltown H won the Player of the Year award Shamrock Rovers#Player of the Year Award recipients
When he became a regular in the first team, Harry proved to be quite impressive but just when everything was going very well he broke his leg against Sligo in a league game at Milltown on October 11, 1981. It was a major setback for H and it took a long time for him to return to his original form. One man's loss is another man's gain, the injury to Harry opened up an opportunity for Peter Eccles who then claimed a regular spot in defence keeping H out of the team.
Harry didn't get much of a look in in Jim McLaughlin's first season in charge, 1983/84, he only made a total of five appearances but he admitted himself it was his own fault. He stalled in renewing his contract and although he had played quite well in a few pre-season friendlies he had kept McLaughlin waiting and that led to H losing his place to Anto Whelan.
If H missed out on a league winners medal in 83/84 he made up for it the following year when he won 2 league medals! With both the first and second teams winning their respective leagues Harry had made enough appearances for both teams to claim a medal for both. To add to that he won two more league medals and three FAI Cup's as Rovers continued to dominate the league right through to 1986/87. In addition to schoolboy and youth international honours Harry has also been capped by the League of Ireland at Inter League and played in 7 1988 Summer Olympics qualifiers.
Perhaps the shortest game of his entire career happened at Dalymount Park on January 19, 1986 when he was red carded after just 4 minutes after a brief altercation with Tom Conway (footballer).
He scored his first goal for the Hoops on the 3rd of December 1980 in a Leinster Senior Cup semi final loss to UCD. He also scored the first goal from the penalty spot in the 1987 FAI Cup Final.
In 1982 Harry spent 6 months at Vancouver Whitecaps.
On the 3rd of June 1990 Harry had a testimonial luncheon in his honour which was attended by members of Ireland's UEFA Euro 1988 squad which included ex teammate Liam O'Brien.
Harry's final appearance was at the RDS against Dundalk on the 15th of April 1991. It was his 300th competitive appearance in the green and white.
He then joined Drogheda United where he played for 2 seasons before retiring. The move was not without controversy however
His first game against Rovers resulted in a win and the subsequent sacking of Noel King.
Harry's family are steeped in Rovers tradition. His father in law is Hughie Gannon who won the FAI Cup with Rovers in 1955 and his younger brother Mark Kenny played for the Hoops in the late 90s.
At the 2007 Shamrock Rovers Player of the Year Awards Harry Kenny was the Hall of Fame recipient.