Definitely Compatibilist.
St. Thomas Aquinas and the Medieval Scholastics who heavily shaped modern theological concepts are considered Compatibilist philosophers. Libertarian philosophy fully rejects a possibility for free will to operate fully with outside influence. This rejects the influence of Grace and every free act, therefore, begins and ends with the human person. Compatibilist free will deals not with the act itself but the
motivation for undertaking the act. Grace is able to provide the agent with the ability to freely assent. The good of the action and God’s intended result will come about however man chooses to deal with the individual act (e.g. when good comes out of an evil action). It is in the agent’s free assent to the act and the outcome which God has ordained that free will comes to its completion.
I believe that it was St. Thomas Aquinas who put it this way, “We are only truly free when we freely choose the good.”
Also, while we’re on the subject, does chance and luck exist? Or is everything that happens in life the result of Divine Providence and the Free Will of Angels and Human Beings?
Chance does exist. It is inherent in the effects of the Fall of Man on Creation. What was once in perfect harmony now becomes discordant through the corruption which came into the world in the Fall.
Luck, however, does not exist. It is generally considered a force outside of the natural (fallen) world which can influenced one way or another whether through superstition (lucky charms) or the natural wheel of fate (fluctuations between bad and good luck).
While chance does exist inherently in the current form of nature, it does not mean that the Lord is not working through the chance of fallen creation to bring about desired end. We must always remember that God is
Super -natural, that is, above the order of the natural world and as such, that order conforms to His will. An example of this would be someone winning the lottery. The natural chance fell to that person. This does not mean that God ordained that chance to fall as it did and that there is not a greater purpose for that prize than simple chance.