It surprises me when people say Chapel doesn’t have a trait, personality, or plotline other than being Spock’s love interest... Let me list all the things we know and have seen about this amazing character.
Christine Chapel is a nurse on The Enterprise. She is on civilian exchange from the Stanford Morehouse Epigenetic Project. She is also a part of Starfleet’s initiative to better observe alien cultures without contamination.
M’Benga treats her as an equal. Pike called her “doctor” in the very first episode which suggests that her medical knowledge and experience must be impressive.
She is an expert on genetic modification. She can mess with your genome and temporarily turn you into an Alien. And she makes it look easy.
She is also interested in archeological medicine. She is doing fieldwork, making discoveries, and writing papers on the subject while doing her other duties on the ship.
Long story short she is quite the genius!
She is outgoing, friendly, witty, funny, adventurous, strong, brave but also compassionate and emotional.
She doesn’t judge, she accepts people for who they are.
She is confident in her abilities. She doesn’t take anyone’s BS. “I don’t think the Vulcan Fellowship is ready for me”… No one, not even Vulcans can bully or make her feel insecure.
But when she was a kid she was bullied. Milo, her Malamute, bit one of those bullies. Good boy!
As it was implied in one of the episodes she is most probably bi.
She has a vulnerable side. She is afraid of commitment. Afraid of romantic relationships getting deep. Perhaps even afraid of falling in love. She uses humor when things get too serious or personal for her. There is a story waiting to unfold in time. And i can’t wait to know more of it!
She was in the Klingon War with M'Benga. They witnessed the ugly face of war and had to make some hard decisions. They used (perhaps even developed) an illegal serum that temporarily gives them enough power and stamina to survive against Klingons. This left a scar on her as much as it did on M'Benga. We will revisit this story in episode 8 (i guess).
She knows how to fight. She is a quick thinker during stressful situations. And she is a badass. For example, she can handle space pirates and all she needs is a hypospray! She can deal with baby Gorns and survive!
She is heroic. She would jump into space without an EV suit to prevent a war.
Oh and she is also Spock's love interest and it's a delicious relationship that enrichens both characters.
This is what we got in 15 episodes. I'm sure we'll learn more about her and she will get new storylines in the seasons to come.