Dual-beam fiber trapping is a versatile technique for manipulating microparticles. We fabricate and evaluate the performance of a compact trap-on-a-chip design and demonstrate, for what we believe is the first time, trapping of low-contrast (m<1.005) lipid vesicles in solution. Counterpropagating fibers are fixed along the chip channel, and we calibrate the trap by optically displacing polystyrene microspheres from the trap center. Measured scattering forces are ~30-49 pN from each beam. Stable trapping and reversible deformation of lipid vesicles is demonstrated under femtonewton trapping forces. This chip has applications in probing a variety of soft biomaterials, such as biological cells, lipid membranes, and protein assemblies.