Sure, it’s a chemical reaction. Every thought you think and every feeling you feel is because something happens in your brain.
There are some neurotransmitters that have been associated with love, like serotonin, dopamine, oxytocin, and vasopressin. And there are brain regions that have activity associated with love, including structures important to memory, pleasure, and emotion.
What it means to have chemistry with another person is an interesting question. I think a lot of times people just mean it metaphorically—but (what I’m about to say is kind of a stretch scientifically)—it’s possible that chemicals secreted by someone else can affect the way you react to them. Have you ever heard of pheromones? They’re chemical signals that animals use to communicate, and they’re important for sexual attraction in some animals. There is some evidence (although it’s limited and controversial) that humans can also use pheromones as part of sexual attraction.
For what it’s worth, I think the idea that love is a chemical reaction in your brain doesn’t make love any less awesome. It just makes chemical reactions in your brain more awesome.