Although general mechanisms of RNA folding and catalysis have been elucidated, little is known about how ribozymes achieve structural stability at high temperature. A previous in vitro evolution experiment identified a small number of mutations that significantly increase the thermostability of the tertiary structure of the Tetrahymena ribozyme. Because we also determined the crystal structure of this thermostable ribozyme, we have for the first time the opportunity to compare the structural interactions and thermodynamic contributions of individual nucleotides in a ribozyme. We investigated the contribution of five mutations to thermostability by using temperature gradient gel electrophoresis. Unlike the case with several well-studied proteins, the effects of individual mutations on thermostability of this RNA were highly context dependent. The three most important mutations for thermostability were actually destabilizing in the wild-type background. A269G and A304G contributed to stability only when present as a pair, consistent with their proximity in the ribozyme structure. In an evolutionary context, this work supports and extends the idea that one advantage of protein enzyme systems over an RNA world is the ability of proteins to accumulate stabilizing single-site mutations, whereas RNA may often require much rarer double mutations to improve the stability of both its tertiary and secondary structures.