Born October 25, 1851 in Douglas, Massachusetts to Irish immigrants Patrick Brannock and the former Kate Heffernan, Brannock’s family soon moved to Chicago after a brief stop in Connecticut.  The fifth of six children (and the first to have been born in the US), Brannock picked up the game in the local lots, joining many of the very good amateur and semi-professional nines in the city for at least a decade. Among them, he played for both the Aetna Club and the Liberty Club (in fact, joining the latter meant he was expelled from the former – even though he wasn’t a member).  He also attended Notre Dame in South Bend and played ball there. In 1870, Brannock was pitching for a local team in Chicago and earning praise for his work:

“Little Brannock of the Actives of this city, stands head and shoulders above Hoy as a pitcher.  The Chicago management have not secured the services of either Hoy or Brannock, but of the two, the latter is certainly the most preferable.” – “Pitchers,” Chicago Tribune, August 15, 1870: 4.

(I don’t know who Hoy was – but he never played in the majors…)

Brannock was a smallish 5′ 8″ but a thick 162 pounds, according to Baseball-Reference.com.

In September, 1871, Brannock played right field and hit well in an exhibition game against the Chicago White Stockings of the National Association. Making a decent enough impression, Chicago hired Brannock to play three games at the end of the 1871 season. Brannock wasn’t kept around and he returned to the amateur game. However, he was asked to fill in at third base for the 1875 White Stockings on August 27th and August 28th.  Brannock appeared in five total games getting just one hit and scoring two runs in each season.  Brannock returned to amateur teams, though he did travel outside the Chicago area some. For example, he was added to the roster of a team in Springfield, Ohio and then Racine, Wisconsin in 1877.

After his baseball days, he worked as a cattle driver in the city. At the time of his death, he was a stable keeper for a local livery and still living at home with his parents.

On October 7, 1881, Brannock died of a hemorrhage in his lungs a couple of weeks shy of his 30th birthday – the Chicago Tribune spelled his last name the way his parents did when they came from Ireland (Brenock). He was buried in Calvary Catholic Cemetery in Evanston, IL. 

Notes:

Baseball-Reference.com
FindAGrave.com
Notre Dame Archives
1860, 1870, 1880 US Census

“Base Ball,” Chicago Tribune, September 24, 1871: 3.
“The City,” Chicago Evening Post, May 1, 1872: 1.
“The Case of Brannock,” Chicago Tribune, May 5, 1872: 9.
“Sporting News,” Chicago Tribune, August 28, 1875:9.
“Base Ball,” Chicago Tribune, August 29, 1875: 9.
“Semi-Professionalisms,” Chicago Tribune, May 20, 1877: 7.
“The Racine Revolution,” Chicago Tribune, June 10, 1877: 7.
“Deaths,” Chicago Tribune, October 8, 1881: 8.