The "SP Challenge" is the deliberately provocative theme of this paper: that the "SP System" (SPS), meaning the "SP Theory of Intelligence" and its realisation in the "SP Computer Model", is more promising as a foundation for the development of human-level broad AI, aka 'artificial general intelligence' (AGI), than any alternative. In that connection, the main strengths of the SPS are: 1) The adoption of a top-down, breadth-first research strategy with wide scope; 2) Recognition of the importance of information compression (IC) in human learning, perception, and cognition -- and, correspondingly, a central role for IC in the SPS; 3) The working hypothesis that all kinds of IC may be understood in terms of the matching and unification of patterns (ICMUP); 4) A resolution of the apparent paradox that IC may achieve decompression as well as compression. 5) The powerful concept of SP-multiple-alignment, a generalisation of six other variants of ICMUP; 6) the clear potential of the SPS to solve 19 problems in AI research; 7) Strengths and potential of the SPS in modelling several aspects of intelligence, including several kinds of probabilistic reasoning, versatility in the representation and processing of AI-related knowledge, and the seamless integration of diverse aspects of intelligence, and diverse kinds of knowledge, in any combination; 8) Several other potential benefits and applications of the SPS; 9) In "SP-Neural", abstract concepts in the SPS may be mapped into putative structures expressed in terms of neurons and their interconnections and intercommunications; 10) The concept of ICMUP provides an entirely novel perspective on the foundations of mathematics; 11) How to make generalisations from data, including the correction of over- and under-generalisations, and how to reduce or eliminate errors in data. There is discussion of how the SPS compares with some other potential candidates for the SP-Challenge. And there is an outline of possible future directions for the research.