The relative contributions of adaptive selection and neutral drift to genetic change are unknown but likely depend on the inherent abundance of functional genotypes in sequence space and how accessible those genotypes are to one another. To better understand the relative roles of selection and drift in evolution, local fitness landscapes for two different RNA ligase ribozymes were examined using a continuous in vitro evolution system under conditions that foster the capacity for neutral drift to mediate genetic change. The exploration of sequence space was accelerated by increasing the mutation rate using mutagenic nucleotide analogs. Drift was encouraged by carrying out evolution within millions of separate compartments to exploit the founder effect. Deep sequencing of individuals from the evolved populations revealed that the distribution of genotypes did not escape the starting local fitness peak, remaining clustered around the sequence used to initiate evolution. This is consistent with a fitness landscape where high-fitness genotypes are sparse and well isolated, and suggests, at least in this context, that neutral drift alone is not a primary driver of genetic change. Neutral drift does, however, provide a repository of genetic variation upon which adaptive selection can act.