In theory I'd be okay with it if the crime was 100% proven beyond even the legal standard. I'm talking on a scientifically observable standard. Full DNA verification, clear recording of the crime, multiple witnesses, etc... beyond a shadow of a doubt.
But life hardly operates on that level of 100% certainty. Evidence gets tampered with or planted, witnesses can misremember, confessions can be coerced, and even DNA results aren't fool-proof. No innocent person should meet their maker because of flaws in the system (and unfortunately they have).
It's better in the long run if the capital punishment option doesn't exist. Better the 1/1000 innocent person sit in jail for a while and then get released with a payday instead of getting put to death and sending the cheque to the grieving family. EVEN if 999/1000 actual cold-blooded killers also avoid the chair. It's worth it for the 1.