Usually, in a debate like this, there is usually someone with whom I can agree, but it seems like everyone here is off in at least one regard, dealing with the issue of historical fact. What you deal with it, is just your opinion...
Slavery exists today, in every country in the world. There are probably as many slaves in America as anywhere else. Slavery will always be around because it is so profitable. Simply being illegal has never stopped slavery (today called human trafficking). Many people turn a blind eye to it because its easier to ignore, especially as most slaves today are prostitutes or children.
Slavery has always existed, and in virtually every culture. What has varied is the conditions in which one comes to be a slave, the status of slaves, the amount of rights a slave has, and the cultural expectations of slave owners.
The Americas, prior to the abolition of slavery in the US and British Empire, used a rather different kind of slavery than the slavery used in other times. It was a concept developed by the Muslims in Africa. Perpetual inherited chattel slavery. This is the slavery most of us are familiar with, and is considerably worse than the other varieties, except perhaps modern sex trafficking. A slave is sold, has no rights, is property like ox, and the worst bit of all...his status as a slave will be inherited by his children, and their children, and so on...
Historically, slaves were usually taken as prisoners of war (the preferable alternative to the also common extermination of the populace). There was no bankruptcy in the ancient world. If you couldn't pay, you, and perhaps your family would be taken as slaves until the debt was paid. From a certain lens, this is more honorable than how we treat money in our society.
In some cultures, slaves could have relatively high status, being in service to a great noble, and as such having a much better quality of life than they could have had they been free. In many cultures, slavery was not permanent...Romans often granted freedom to favored slaves in their wills.
Then there is the issue of treatment. One could make the argument, and the slave owners in the South certainly did, that the slaves had a better life on the plantations than the free Irishmen working in the factories up North. A slave was guaranteed food and and a pension, and most owners made sure they were healthy. A factory worker worked with no insurance in an extremely dangerous and unhealthy environment for just a few pennies a day.
As has been pointed out, serfdom is its own kind of slavery. A serf has few rights, does not own property, is exploited for his labor by the lord of the manor, and is prohibited by law from leaving the land. This manorial system, however unfair, was something of a social contract though..the lord treats them not too badly and protects them from vikings and such (or orcs) and his own profits thereby, and they won't cause a fuss.
Finally, I'd like to note that the ancient Greeks and Romans had highly sophisticated cultures, and advanced ideas about philosophy...ancient man was not less intelligent than modern man, they just lacked modern technology. Though I would not endorse Greek or Roman ethical codes, it is a poor argument to say that they were unenlightened. Perhaps the fact that they new what they were doing when they put whole cities to the sword makes it all the more terrible.
As for the question itself...I would say that slavery can be practiced by a person of any alignment depending on the laws, the culture, and the treatment. However, Lawful Evil fits best and Chaotic Good fits worst. Slavery is usually an institution that is legal, and undermining the institution (i.e. killing a slave owner and freeing his slaves) would be breaking the law. What one does about the laws in question determines the law or chaos question. What the laws are depends on the campaign. What sort of slavery it is largely going to be dependent on the DM. Ownership of slaves, why the slaves are owned, and how the slaves are treated determines the good-evil axis. Slavery in itself is never good, but could be either neutral or evil, depending on the circumstances.
TLDR: Slavery is very old and has existed everywhere, in every time, but isn't always the same. It's not as simple as some are making it out to be. This isn't a black and white question. Freeing lawfully owned slaves is chaotic. Owning slaves if they're well treated is neutral. Owning them and treating them badly, or making slaves of people, is evil.
