Is there anything else running in the background? Are you saying that with Chrome the CPU is working at 35% - 50% when you are using the browser, then when you click a link it goes to 100%, then drops back down to 35% - 50% again?
If that's the case then something is definitely wrong. With my quad core CPU, FireFox uses between 0% - 4% when I am viewing a website. Clicking a link to go to another website the CPU will go to 20% and then drop back down to 0% - 4%. Have you tried using Internet Explorer or another browser (like Firefox)?
If your CPU spikes only when using Chrome, then uninstall it and re-install a current version. If Internet Explorer does that too, then your Windows OS might be a little unstable or have some type of issues like a bloated Registry that is causing your laptop to be a bit sluggish.
You can try a free program called CCleaner to help delete junk in the Registry. But if the problem persists, then you may want to consider reinstalling Windows. Backup important data first though.