Trashing two birds with one stone
No. Once the first paid ability is triggered, it resolves completely before another paid ability can be triggered. The exceptions are "prevent" and "avoid" abilities. So, in your example either ability will result in the Cortez Chip being in the Heap and no longer installed before you could possibly trigger the other ability. The specific text from the rulebook that applies:  


  Once an ability is triggered, its effect is resolved immediately and
  can only be stopped by prevent or avoid effects.