A systolic array for inverting an n × n matrix using a Monte Carlo method is proposed. The basic array computes a single row of the inverse in3n + N + Tsteps ( including input and output time) and O( nNT) cells whereNis the number of chains andTis the length of each chain in the stochastic process. A full inverse is computed in the same time but requires O(n2NT) cells. Further improvements reduce the time to3n/ 2 + N + Tusing the same number of cells. A number of bounds onNandTare established which show that our design is faster than existing designs for reasonably large values ofnIndeed the final arrays require less than n4cells and have a computing time bounded above by 4n.