That carbon is connected to three other carbons, and a secret hydrogen in the back. Well thank goodness that hydrogen is the lowest priority and it is in the back, so we won't have any shenanigans later. Let's call the three carbons LEFT, RIGHT, and TOP. Since they are all carbons, they are all tied, and we will have to examine what these carbons are connected to.
Looking forward, LEFT is connected to an oxygen, a carbon, and a hydrogen. OCH.
TOP is connected to an oxygen and two hydrogens. OHH.
RIGHT is connected to an oxygen, a carbon, and a hydrogen. OCH.
They all have an oxygen as their best candidate, but when looking at their second best atom, TOP submits a hydrogen while LEFT and RIGHT contribute a carbon. TOP is therefore below LEFT and RIGHT, and we'll give it priority 3. Onward...
LEFT's carbon is connected to an oxygen, another oxygen, and a hydrogen. OOH. Remember we count each bond individually.
RIGHT's carbon is connected to a carbon and two hydrogens. CHH.
Looks like LEFT wins and is priority 1. RIGHT is priority 2.
So the priorities in order are LEFT -> RIGHT -> TOP -> BEHIND.
left -> right -> top is in the counterclockwise direction.
This chiral carbon is S.
The book was correct.