As a professional nerd, I'm extremely skeptical that either Chrome or Firefox (or Safari or Opera) ships with malware. My fellow nerds may have done something, added some feature that someone else calls 'malware', but it wouldn't fit my definition.
When you download *anything*, **anything**, have your AntiVirus scanner running and updated. Have Malwarebytes running (or Spybot).
Make sure you download the software from a reputable source - it's common for other hacker sites to take a Chrome or Firefox, infect it, and then post it for downloading.
Remember what you pay for some very marvelous software: $0.00.
Caveat Emptor!!!