We report the results of studies, using digital video microscopy, of the spatial distribution of particles in a quasi-one-dimensional colloidal liquid. The system studied consists of a water suspension of silica particles with diameter sigma=1.58 mum confined in a 3 mumx3 mumx2 mm silicone elastomer channel. The measured spatial distributions have been characterized by the nearest-neighbor distribution function and the pair correlation function, and the pair correlation function has been inverted, using the hypernetted chain approximation, to yield the effective colloid-colloid interaction. The effective colloid-colloid interaction is found to have an attractive potential well with depth of similar to0.3k(B)T at a colloid-colloid separation Rapproximate to1.18sigma. Molecular-dynamics simulations of the nearest neighbor and pair correlation functions carried out using the empirically determined colloid-colloid interaction are in very good agreement with the experimental data. The experimental data obtained rule out any important charge-charge contribution to the measured colloid-colloid interaction. It is suggested that because the host liquid does not wet the channel wall, and the colloid particles are tightly confined in the long narrow channel, capillary forces determine the effective colloid-colloid interaction. This suggestion is consistent with the determination (also reported) that the effective colloid-colloid interaction in a quasi-two-dimensional suspension of the same particles is different from that in the quasi-one dimensional suspension.