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In this paper, we describe the development and physics results of a fully-kinetic capability of the PIC code Chicago to model, initially in 1D, proton-driven fast ignition scenarios, in which a pre-compressed fusion target is heated by a high-energy proton beam. All particle species are fully kinetic, and both inter- and intra-species collisional interactions are handled by a binary collision model developed for PIC codes for macroparticles of arbitrary weights. Fusion reactions are also treated in a fully binary fashion. Electric fields are accounted for by an implicit static field solution. Radiation may be included either in an optically-thin approximation, or in conjunction with a multi-group diffusion model for radiation transport. Macroparticle numbers in the simulation can be controlled by an adaptive collapse algorithm which attempts to preserve the local velocity distribution function of the species. The model is demonstrated initially with (equimolar) DT and compared to results obtained by radiation-hydrodynamic codes. We then present some results for proton-boron targets in a preliminary effort to map out the potential burn space of this fuel.