A strong signal for double parton (DP) scattering is observed in a 16 pb(-1) sample of <(p)over bar p> --> gamma/pi(0) + 3 jets + X data from the CDF experiment at the Fermilab Tevatron. In DP events, two separate hard scatterings take place in a single <(p)over bar p> collision. We isolate a large sample of data (similar to 14 000 events) of which 53% are found to be DP. The process-independent parameter of double parton scattering, sigma(eff), is obtained without reference to theoretical calculations by comparing observed DP events to events with hard scatterings in separate <(p)over bar p> collisions. The result sigma(eff) = (14.5 +/- 1.7(-2.3)(+1.7)) mb represents a significant improvement over previous measurements, and is used to constrain simple models of parton spatial density. The Feynman x dependence of sigma(eff) is investigated and none is apparent. Further, no evidence is found for kinematic correlations between the two scatterings in DP events