We implement a noiseless optical amplifier using a phase-sensitive four-wave mixing process in rubidium vapor. We observe performance near the quantum limit for this type of amplifier over a range of experimental parameters and show that the noise figure is always better than would be obtained with a phase-insensitive amplifier with the same gain. Additionally, we observe that the amplifier supports hundreds of spatial modes, making it possible to amplify complex two-dimensional spatial patterns with less than a 10% degradation of the input signal-to-noise ratio for gains up to 4.6. To confirm the multimode character of the amplifier, we study the noise figure as a function of spatially-varying losses. Additionally, we investigate the spatial resolution of the amplifier and show that it supports a range of spatial frequencies from 1.3 to more than 35 line pairs per millimeter.