Gbp1p is a putative telomere-binding protein from Chlamydomonas reinhardtii that contains two RNA recognition motifs (RRMs) which are commonly found in heterogeneous nuclear ribonucleoproteins (hnRNPs). Previously we demonstrated that Gbp1p binds single-stranded DNA (ssDNA) containing the Chlamydomonas telomeric sequence but not the RNA containing the cognate sequence. Here we show that at lower protein concentrations Gbp1 can also bind an RNA containing the cognate sequence. We found that mutation of the two RRM motifs of Gbp1p to match the highly conserved region of hnRNP RRMs did not alter the affinity of Gbp1p for either RNA or DNA. The ability of Gbp1p to associate with either of these two nucleic acids is governed by the dimerization state of the protein. Monomeric Gbp1p associates with either ssDNA or RNA, showing a small binding preference for RNA. Dimeric Gbp1p has a strong preference for binding ssDNA and shows little affinity for RNA. To the best of our knowledge, this is the first example of a protein that qualitatively shifts its nucleic acid binding preference upon dimerization. The biological implications of a telomere-binding protein that is regulated by dimerization are discussed.