Nearly all classes of coding and non-coding RNA undergo post-transcriptional modification, including RNA methylation. Methylated nucleotides are among the evolutionarily most-conserved features of transfer (t)RNA and ribosomal (r)RNA1,2. Many contemporary methyltransferases use the universal cofactor S-adenosylmethionine (SAM) as a methyl-group donor. SAM and other nucleotide-derived cofactors are considered to be evolutionary leftovers from an RNA world, in which ribozymes may have catalysed essential metabolic reactions beyond self-replication3. Chemically diverse ribozymes seem to have been lost in nature, but may be reconstructed in the laboratory by in vitro selection. Here we report a methyltransferase ribozyme that catalyses the site-specific installation of 1-methyladenosine in a substrate RNA, using O6-methylguanine as a small-molecule cofactor. The ribozyme shows a broad RNA-sequence scope, as exemplified by site-specific adenosine methylation in various RNAs. This finding provides fundamental insights into the catalytic abilities of RNA, serves a synthetic tool to install 1-methyladenosine in RNA and may pave the way to in vitro evolution of other methyltransferase and demethylase ribozymes.