Short term memory is famously limited in capacity to Miller's (1956) magic number 7 plus or minus 2--or, in many more recent studies, about 4 plus or minus 1 "chunks" of information. But the definition of "chunk" in this context has never been clear, referring only to a set of items that are treated collectively as a single unit. We propose a new more quantitatively precise conception of chunk derived from the notion of Kolmogorov complexity and compressibility: a chunk is a unit in a "maximally compressed" code. We present a series of experiments in which we manipulated the compressibility of stimulus sequences by introducing sequential patterns of variable length. Our subjects' measured digit span (raw short term memory capacity) consistently depended on the length of the pattern "after compression," that is, the number of distinct sequences it contained. The true limit appears to be about 3 or 4 distinct chunks, consistent with many modern studies, but also equivalent to about 7 uncompressed items of typical compressibility, consistent with Miller's famous magical number. (Contains 11 figures and 1 table.)