Česnauskis earned a move to the Russian Premier League before his nineteenth birthday, when he joined Dynamo Moscow in 2000.
The terms of this deal involved him signing for FBK Kaunas and being immediately loaned to the Edinburgh side for three seasons.
[6] On 26 February 2009, Česnauskis said he would leave Hearts in the summer unless he was given first team football before the end of the season, having started just two matches.
[7] On 27 April, it was confirmed with immediate effect that Česnauskis and his fellow Lithuanian teammate Saulius Mikoliūnas, left Hearts.
[10] In June 2011 Česnauskis signed a two-year contract with Azerbaijan Premier League side FC Baku.
Česnauskis was released by FC Baku at the end of the 2012–13 season after scoring eight goals in 52 appearances for the club.
With Trakai, he finished runners-up in the 2015 and 2016 A Lyga seasons and reached the final of the Lithuanian Football Cup in 2016, in which his team lost 0–1 against FK Žalgiris after extra time.