A reaction does occur. both CrCl3 and Pb(NO3)2 are soluble in water so they will split up into ions. The double replacement reaction will yield (through inside/outside recombination) PbCl2 and Cr(NO3)3. All compounds with NO3- ions are soluble however, the PbCl2 compound is insoluble. Balancing the equation and eliminating all spectator ions will result in a net ionic equation of: 3Pb+2 + 6Cl- --> 3PbCl2
I hope this answered your question.