To "chip in" means to help with something that a group of people is doing. Sometimes "chipping in" means giving money. In the example above, the speaker wants her friend to "chip in" by giving some money for the gift.
Someone can also "chip in" by volunteering their time or work:
Come on, guys! If we all chip in and help, we'll have this place clean in no time!
"Chip in" is only used to talk about groups of people. Volunteering alone to help someone isn't really "chipping in".