Vondra was born in Prague. He graduated in geography from Charles University in Prague in 1984, receiving a Doctor in Natural Sciences degree one year later. In the mid-1980s he was a dissident and Charter 77 signatory. After organizing a demonstration in January 1989, Vondra was imprisoned for two months. In November 1989, while the Velvet Revolution was underway, he co-founded the Civic Forum.