A major reason why LFG employs c-structure is because it is context-free. According to Tree-Adjoining Grammar (TAG), the only context-sensitive operation that is needed to express natural language is Adjoining, from which LFG functional uncertainty has been shown to follow. %as a corollary. Functional uncertainty, which is expressed on the level of f-structure, would then be the only extension needed to an otherwise context-free processing of natural language. We suggest that if f-structures can be derived context-freely, full-fledged c-structures are not strictly needed in LFG, and that chunks and dependencies may be sufficient for a formal grammar theory. In order to substantiate this claim, we combine a projection of f-structures from chunks model with statistical techniques and present a parser that outputs LFG f-structure like representations. The parser is representationally minimalist, deep-linguistic, robust, fast, and has been evaluated and applied. The parser addresses context-sensitive constructions by treating the vast majority of long-distance dependencies by approximation with finite-state patterns, by post-processing, and by LFG functional uncertainty.