We report that the incorporation of hydroxide ions (OH)- significantly enhances the superconducting transition temperature (Tc) in the LnFeAsO-based superconductors (Ln1111: Ln = La, Ce and Pr). For La1111, Tc of the (OH)- incorporated sample synthesized using high-pressure technique becomes 35 K, which is higher by 7 K than the typical optimally-doped La1111 superconductors. Similar enhancement in Tc is also observed for Ce1111 and Pr1111. 1H-NMR measurement have confirmed the existence of hydrogen atoms in the samples. Accompanying the (OH)- incorporation, the lattice parameters are largely contracted, down to the values which have never been attained by any other dopings/substitutions.