We propose a hybrid pulse position modulation/ultrashort light pulse code-division multiple-access (PPM/ULP-CDMA) system for ultrafast optical communications. The proposed system employs spectral CDMA encoding/decoding and PPM with very short pulse separation. The statistical properties of the encoded ULP are investigated with a general pulse model, and the performance of the proposed PPM/ULP-CDMA system is investigated. It is shown that we can improve upon the performance of other ULP-CDMA systems, such as those using on-off keying, by employing PPM. It is also shown that we can improve the performance of the proposed system by increasing the effective number of chips, by increasing the number of PPM symbols, and by reducing the ULP duration. The performance analysis shows that the aggregate throughput of the proposed PPM/ULP-CDMA system could be over 1 Tb/s.