Self-organization of 1,4-benzenedicarboxylic acid molecules (terephthalic acid, TPA) on a rutile TiO2(110)-(1×1) surface is studied by means of ultra-high vacuum scanning tunneling microscopy (STM) and non-contact atomic force microscopy (nc-AFM). When saturation coverage is achieved with the formation of one monolayer, STM images reveal two alternating contrast patterns: (i) a well-organized (2×1) structure and (ii) a mixed structure of molecular rows oriented along the 001 crystallographic direction. Complementary STM images recorded with two different tip terminations prove that the two contrasting patterns indicate the same stable surface structure. The nc-AFM imaging confirms the mixed molecular row structure. It is concluded that TPA molecules are adsorbed in an upright position. This occurs with one of the carboxyl group bound dissociatively in a bi-dentate fashion with the two 5-fold coordinated Ti atoms. The second carboxyl group is exposed to the vacuum interface. This carboxyl terminated surface is discussed in terms of surface chemical functionalization.