We adapt the method of Monte Carlo configuration interaction to calculate core-hole states and use this for the computation of X-ray emission and absorption values. We consider CO, CH 4 , NH 3 , H 2 O, HF, HCN, CH 3 OH, CH 3 F, HCl and NO using a 6-311G** basis. We also look at carbon monoxide with a stretched geometry and discuss the dependence of its results on the cutoff used. The Monte Carlo configuration interaction results are compared with EOM-CCSD values for X-ray emission and with experiment for X-ray absorption. Oscillator strengths are also computed and we quantify the multireference nature of the wavefunctions to suggest when approaches based on a single reference would be expected to be successful.