China's Yang Qian set a new Olympic record as she won the women's 10-metre air rifle final.
Galashina led the race for the gold in the final until she cracked under pressure and signed off with her lowest score of 8.9 for a total of 251.1.
Yang responded to the pressure by firing 9.8 to snatch the gold with an Olympic record of 251.8.
Switzerland’s Christen was further back on 230.6.
Norwegian Jeanette Hegg Duestad had set an Olympic qualifying record of 632.9 to reach the final but finished just outside the medals.
Team GB’s Seonaid McIntosh was knocked out in qualification.
Later on day one, the men's 10m air pistol gold medal will be up for grabs, along with medals in eight other disciplines.
The biggest event on the first day is the men's road race, which features four Team GB representatives in Geraint Thomas, Tao Geoghegan Hart, Adam Yates and Simon Yates.