Is chivalry dead?

I often wonder…
I walked out of my second home (Starbucks) the other day and this seemingly excessively happy man held the door open for me. I thanked him and he smiled and declared “Chivalry is not dead”.
Does this prove chivalry? What is chivalry? I think of it like this:

But if you look at synonyms for it they are gallantry, good manners, courtesy, politeness and the dictionary says, “The medieval system, principles, and customs of knighthood”.
Are women allowed to be chivalrous? I hold the door open for people. I think it’s a nice thing to do for other people, but I certainly wouldn’t want to be knighted for it. Were women not allowed to hold the door open in medieval days?
Personally I think being chivalrous means over and above expected proper behavior from MEN. I don’t really expect anyone to hold the door for me, but I am grateful when someone does. However I have seen just as many women hold the door for men as men do for women. If I were to describe a man as chivalrous he would have to open the car door for me or slay a dragon and since we don’t have any dragons in MN maybe protect me from sitting alone in a restaurant.
Let’s be candid here for a moment. Do women need protection? As a woman in the 21st century I can have a career, make money, vote, carry pepper spray, and I don’t walk at night down scary alleys. Most days the most protection I need is from my cat waking me up at 4 in the morning because she’s hungry.