As someone who wants equality for all, nah.
Completely agree with EVERYTHING Nikotinic said and found it extremely insulting personally before I knew what trans even was, thinking I was a capable female human and they were assuming I could handle heavy things, or afford to pay for anything. I can sure as hell manage a simple chair! And so on. Unless I was actually struggling with something, I hated people assuming I couldn't do that something. Being female bodied isn't a disability. Now true, I wasn't actually a girl, but I did talk about hating that sort of thing with girls who agreed and hated it themselves.
Personally, I'm interested in the type of girls who think the same so not appearing chivalrous doesn't concern me.
However, girls can sometimes play a game early on and for that, I play along. Example: if a girl is cold, I'll give her my coat, but she best believe if she makes a habit of that I'll start telling her to bring a coat when we go out and if not, just dump her because to me that's just being stupid. I can see that as being a way to test a guy early on to see if they're giving and receptive to their needs and hints, and yeah, I'll play that game. Now and again as a rarity is fine, but when it becomes habit, no! The way I see it women should have some self respect and intelligence; if it's cold out, wear a coat! This may be more of a concern to me as someone living in Canada. It can get VERY cold here! We had up to -20 degree celcius weather recently. In weather like that, I'm choosing pre-planned warmth over chivalry for a silly girl!

It's kinda old fashioned to be chivalrous really and as such I feel you're more likely to lose than win with chivalrous behaviour. It can depend on the type of girl you want to be fair. For me I want an equal and she shouldn't care about that stuff and perhaps not even want it. For me, there's nothing sexier or appealing than a girl who holds a door open for me if she happens to get there first or insist on splitting costs of a night out. That's a girl to hang onto! There's some obvious things that are more common sense. Going back to the door example, if I open the door, I hold it for anyone I'm with regardless of gender. I never open a door and go straight through unless I'm on my own. If anyone is struggling with something I'll offer to help, boy or girl. I've told elderly men and women in a bus queue to go ahead an sit down, I'll make sure to keep their place and so on. I'll tell able bodied people to move for any disabled or elderly individuals on public transport if they're too shy to say themselves. In this day and age, I find chivalry can often be unwanted and more of an insult to many girls.
Oh, and on public transport, unless I'm interested in the girl and looking for a way to start a conversation

, length of time standing wins when it comes to who gets the seat. If I'm next to a girl who got on 1 stop ago and I've been there 15 minutes and a seat frees up in front of me. Sorry, I win! Lol. Unless you obviously need it (disabled/elderly) it's fair game really.
My opinion: equality trumps chivalry.