A method for constructing a description of a large N-electron system from explicitly correlated calculations on O(N) overlapping subsystems is developed. One- and two-electron reduced density matrices for the system are constructed using the reduced density matrices obtained from explicitly correlated calculations on the subsystems. This "locally correlated reduced density matrix" method is closely related to divide-and-conquer treatments of mean-field and density-functional theory, and to wave-function-based O(N) treatments of correlation. Calculations on toy systems indicate that the method recovers a complete description of local correlation effects, is size extensive, and can be formally linear scaling.(C) 2003 American Institute of Physics.