After a year in the F-youth of TSV Wendelstein, Tschauner began his career in 1995 with the first 1. FC Nürnberg, where he went through all youth teams. Having already partially helped in the 2003/04 season in goal for the second team of the FCN, he was the third goalkeeper in 2004/05 for the pros and goalkeeper of Bayern League team 1. FC Nuremberg. On 22 October 2005 Tschauner's first game in the Bundesliga was against Arminia Bielefeld.
TSV 1860 Munich
In the summer of 2006 he moved to 1860 Munich, where he signed a three-year contract. During the 2006/07 season he served as the Regionalliga Süd U23 Lions goalkeeper, and made five appearances in the second division team of 1860 Munich, where he twice replaced Michael Hofmann, who had been injured. In preparing for the 2007–08 season, coach Marco Kurz stated Tschauner would be primary goalkeeper before Hofmann. On match day however, Tschauner suffered a partial tear of the cruciate ligament in his left knee, so Hofmann replaced him. After being in goal for the Sechzger, Tschauner played in the role of the substitute goalkeeper for several months. On 27 February 2008, Hofmann was injured in the Cup derby against FC Bayern, with Tschauner then making a comeback. Afterward, he became the first choice for goalkeeper in the league. In March 2008, his contract was extended until 2011. Tschauner also went into the following season as goalkeeper. But when Uwe Wolf replaced Kurz as coach in February 2009, Tschauner was forced to resign to a secondary role while Hofmann became goalkeeper again. However, Hofmann was again injured after the 30. Gameday, so at the end of the season Tschauner was goalkeeper again. In the summer of 2009, the 1860 Munich took on Gábor Király and immediately declared him as goalkeeper. Tschauner was again assigned as replacement goalkeeper. During the 2009/10 season he played several times for the second team; he only played on the professional team on the final day. In the following season he sat out for 33 games and only played in the last home game. In total Tschauner sat out for 49 league and cup appearances, and was part of five 1860 games and 40 games for 1860 II.
FC St. Pauli
For the 2011–12 season Tschauner joined FC St. Pauli, where he signed a contract until 2013. There, he became an instant goalkeeper and took part in all 19 league games until in the last game before the winter break—a 2: 0 win over Eintracht Frankfurt—he sustained an acromioclavicular injury, which made him unfit to play for several weeks. On 1 April 2013, during the 27th round of the Bundesliga 2, Tschauner scored in the 90th minute of the 2:2 final against SC Paderborn 07 with a header after a corner kick from midfielder Dennis Daube.
Hannover 96
On 14 May 2015 Tschauner signed a contract with the Bundesliga club Hannover 96. On 2 January 2019, It was announced that he would join FC Ingolstadt on loan until the end of 2018–19 season.
RB Leipzig
On 30 July 2019, Tschauner joined RB Leipzig on a two-year contract.
International career
Tschauner played ten times for the youth teams of the DFB. In 2004, he was on reserve for the U-19 European Championship. He later played in the U-20 team a total of nine times, and was also part of the German squad at the 2005 World Junior Championships. Tschauner also played as part of the U21 team on 15 August 2006 against the Netherlands.