To me definetely no.
In my opinion carrying about women's physical comfort and health more than the men's is NOT honorable, chivalrous, gentlemanly or something good and doesn't mean treating women than men. People doesn't exist entirelty separately from each other and mostly don't care only about themselves and don't want physical comfort only for themselves. I believe this doesn't apply only to particularly kind and selfless people, I am far from kindest person in the world or even in this club but said applies to me. By putting men's life and health in danger you DO hurt and mistreat women even if indirectly because most of men are valued and loved by some females who maybe even value those men more than their own physical comfort. When one human being is hurt directly, this being isn't the only victim but all people who love and value him.
No, I refuse to give any credit to Beast for this and in Belle's situation I would feel zero gratitude for getting own bedroom and I would consider this act rather self-deception than chivalry.

I do think the Beast does has some small kernel of kindness in him even at the beginning of the movie, but I don't think him giving Belle a nice room is any indication of it. He only does that because he knows she's his only chance to break the curse, not because he's trying to be kind to her for kindness' sake. If she had been a boy, she would have gotten thrown in the dungeon the same as Maurice.

To me, the only moment when I see some humanity in Beast that early in the film is right after Belle sacrifices herself for her father and he asks "...you would do that for him?" I think Beast thought there was no kindness left in the world, but Belle's action shocks and surprises him because it is such a selfless act born out of love. His tone of voice changes so much when he says this, and I think that is the small, scared man deep inside him grasping on to hope for the first time in years.

Lumiere is the gentleman behind the idea. He advised the Beast to do that. Beast only did it because Belle’s emotional state made him feel guilty. Up until then he was happy to leave her in the tower.

Not necessarily. I think he did it just because she might break the curse, in which case, it'd be best to at least give her a nice room to stay in. And as others said, it was Lumiere's idea.
I don't think the gentlemanly side of him really appears until he defends Belle from the wolves.

What PrincessAyeka said. Beast is faaaar from a gentleman.

Early on he is just following the advice of his servants. He doesn't start to act like a gentleman until much later in the movie.