We develop an approximation for the probability of optically resolving two fluorescent labels on the backbone of a DNA molecule confined in a nanochannel in the Odijk regime as a function of the fluorescence wavelength, channel size, and the properties of the DNA (persistence length and effective width). The theoretical predictions agree well with equivalent data produced by Monte Carlo simulations of a touching wormlike bead model of DNA in a high ionic strength buffer. Although the theory is only strictly valid in the limit where the effective width of the nanochannel is small compared with the persistence length of the DNA, simulations indicate that the theoretical predictions are reasonably accurate for channel widths up to two-thirds of the persistence length. Our results quantify the conjecture that DNA barcoding has kilobase pair resolution-provided the nanochannel lies in the Odijk regime.