The real (n) and imaginary (k) refractive indices of an immobilized monolayer of 27 nucleotide (nt) single stranded DNA (ssDNA) and the corresponding double stranded DNA (dsDNA) are measured in the 255-700 nm range. Multiple techniques are used to obtain consistent estimation. The coverage is similar to6.5% with an average interchain distance of tethered ssDNA molecules of similar to11.8 nm, which is significantly larger than the "footprint" of the chain on the surface. The measured increase in n by similar to5% between the ssDNA and the dsDNA is 20% smaller than the expected change due to doubling of the molecular weight. The change in k is not significant, indicating that the electron delocalization effect expected in dsDNA due to base pair stacking is not important at optical frequencies.