Crystalline silicon samples doped with carbon were irradiated with electrons and subsequently implanted with protons. Infrared-absorption measurements revealed local modes of hydrogen and carbon at 2967.4, 911.7, and 654.7 cm-1, which originate from the same defect. Measurements on samples codoped with different carbon and hydrogen isotopes showed that the defect contains two equivalent carbon and two equivalent hydrogen atoms. From uniaxial stress measurements, the defect is found to display trigonal symmetry. Ab initio local-density-functional theory was applied to calculate the structure and local vibrational modes of defects with pairs of equivalent carbon and hydrogen atoms. Based on these results, the observed local modes are ascribed to a defect with two adjacent substitutional carbon atoms, each of which binds a hydrogen atom located between the carbon atoms.