DEAD-box helicase proteins perform ATP-dependent rearrangements of structured RNAs throughout RNA biology. Short RNA helices are unwound in a single ATPase cycle, but the ATP requirement for more complex RNA structural rearrangements is unknown. Here we measure the amount of ATP used for native refolding of a misfolded group I intron ribozyme by CYT-19, a Neurospora crassa DEAD-box protein that functions as a general chaperone for mitochondrial group I introns. By comparing the rates of ATP hydrolysis and ribozyme refolding, we find that several hundred ATP molecules are hydrolyzed during refolding of each ribozyme molecule. After subtracting nonproductive ATP hydrolysis that occurs in the absence of ribozyme refolding, we find that approximately 100 ATPs are hydrolyzed per refolded RNA as a consequence of interactions specific to the misfolded ribozyme. This value is insensitive to changes in ATP and CYT-19 concentration and decreases with decreasing ribozyme stability. Because of earlier findings that ∼90% of global ribozyme unfolding cycles lead back to the kinetically preferred misfolded conformation and are not observed, we estimate that each global unfolding cycle consumes ∼10 ATPs. Our results indicate that CYT-19 functions as a general RNA chaperone by using a stochastic, energy-intensive mechanism to promote RNA unfolding and refolding, suggesting an evolutionary convergence with protein chaperones.