A new optically transparent, near-infrared-absorbing low energy gap conjugated polymer, poly (thieno[3,4-b]furan) (PT34bF), with promising attributes for photovoltaics is reported herein. PT34bF was prepared electrochemically, and upon redox cycling, doping was found to be anion dominant. The energy gap of the polymer was found to be 1.04 eV as calculated from the low-energy edge of the absorption spectrum of the neutral polymer at -0.6 V and 1.03 eV for the chemically neutralized polymer using hydrazine. The polymer is pale blue in the neutral form and a more transparent pale blue in the oxidized conducting state with photopic transmittances of 62% and 72% (ITO glass substrate not subtracted), indicating the possibility of application as a transparent conductor or an ion-storage layer for electronic devices. Density functional theory (DFT) calculations using B3PW91 hybrid functional have been carried out for possible connections between the three open alpha-positions. In addition to optimizing geometry, band structure properties such as band (energy) gaps, band widths, and effective masses were calculated for each connection. Calculations show that 4-6 connectivity is the most probable and dominant structure for the polymer resulting from T34bF, and the calculated energy gap of 1.01 eV for polymerization via this connection corresponds well with the experimentally observed value of 1.04 eV.