By itself, the word is not at all offensive, but it can be when used to refer to a person.

Not all the time. Some people can take it offensively and some people may think nothing of it. It really depends on the person.

What's important to know is that chubby is a less offensive (nicer) way to say fat.

Yes and no. If it's you talking with another thin person outside of a work setting, you can probably use it without anyone getting offended. If it's you and a fat person, depends. Some fat people are OK with the term and/or use it themselves to describe it. Other fat people, specially those involved in 'fat activism', believe that the word 'fat' should lose the stigma and negative connotation it has, and should be used as you would use the word 'tall'; while terms like 'chubby', being just a 'cute' way to say 'fat', are equally annoying, specially if your reason for addressing someone's body is questionable to begin with. If you use it as an insult, it's of course always offensive. So, TL;DR, no 'get out of jail free' card for this one, and asking the fat people you talk with could let you know if it's a term you can use safely around them. On the terms 'overweight' and 'obese': http://thisisthinprivilege.org/faq#overweight

No. Chubby is just an adjective. Bears are chubby. Babies are chubby. Blah, blah, blah. Call your girlfriend chubby...then you mights haves somes problems.