From first principles calculations, we investigate the stability and physical properties of single layer h-BN sheet chemically functionalized by various groups viz. H, F, OH, CH3, CHO, CN, NH2 etc. We find that full functionalization of h-BN sheet with these groups lead to decrease in its electronic band gap, albeit to different magnitudes varying from 0.3 eV to 3.1 eV, depending upon the dopant group. Functionalization by CHO group, in particular, leads to a sharp decrease in the electronic band gap of the pristine BN sheet to ~ 0.3 eV, which is congenial for its usage in transistor based devices. The phonon calculations on these sheets show that frequencies corresponding to all their vibrational modes are real (positive), thereby suggesting their inherent stability. The chemisorption energies of these groups to the B and N atoms of the sheet are found to lie in the range of 1.5 -6 eV.