We have measured the absolute-rate coefficient for electron-impact excitation (EIE) of C[sup 3+](2[ital s] [sup 2][ital S][sub 1/2][r arrow]2[ital p] [sup 2][ital P][sub 1/2,3/2]) for energies near threshold. A delayed coincidence technique with inclined beams was used. Radiation from the excited ions was detected using an optical system that subtends slightly over [pi] steradians. At an ion-rest-frame energy of 10.10 eV the measured rate coefficient was (7.79[plus minus]2.10)[times]10[sup [minus]8] cm[sup 3] s[sup [minus]1] and the measured cross section was (4.15[plus minus]1.12)[times]10[sup [minus]16] cm[sup 2]. The uncertainties quoted here represent the total experimental uncertainty, statistical and systematic, at a confidence level considered to be equivalent to a statistical 90% confidence level. Good agreement is found with other measurements. Agreement is not good with Coulomb-Born with exchange and two-state close-coupling calculations, both of which fall outside our 90% confidence limits. Nine-state close-coupling calculations are in better agreement. However, the calculations lie at the extreme edge of our uncertainty limits. Taking into account previous measurements of EIE in C[sup 3+] and also a measurement of EIE in Li-like Be[sup +] that falls significantly below theory at threshold, there is a suggestion that the C[sup 3+](2[ital s][r arrow]2[ital p]) EIE rate coefficient near thresholdmore » may fall slightly below presently accepted values.« less