Back to the chivalry topic, I believe that yes, chivalry is benevolent sexism. It's specifically based in the idea that women are delicate, weak flowers that need to be protected by men.
That doesn't mean that doing something considerate like holding open doors or being "gentlemanly" can only be motivated by chivalry. Personally, I love holding doors for people, taking my partner out for a meal, pampering him and making him feel like a princess, killing spiders for him so I feel like a knight in shining armor (pfft). But when I do it, it has nothing to do with whether or not the person I'm interacting with is male or female.