The unedifying exchange, which took place on Tuesday, was filmed by another customer and sent to Chen.
At one point in the video, Chen asks to speak to the manager, only to be told: "You're talking to the manager - get out!"
Melissa demands that somebody call the police, and tells Chen she could be arrested over the cookie straw.
"You're not going to be served, so give me the straw and leave."
Chen posted the clip to Starbucks' Facebook page, which led to Melissa getting fired.
Writing alongside the footage, Chen told how Melissa flew into a rage after she didn't hear something she was asked because she was opening a Starbucks rewards app on her phone.
She said: "Melissa started to shout at me saying 'Hey, helloooo' with a very bad attitude.
"The only thing I said to her is 'sorry I don't hear you but you don't have to yell.' And till now, I haven't figured out which word aggravated her.
"Then she took the scanner away as I was trying to pay then told me to leave and never go back. I was trying to ask other employees who I can speak to.
"She thought I [was] leaving with the straw in my hand (I picked it up before everything happened); she said I am stealing the straw.
"Really?! call me stealing! [sic] I felt so bad for what happened, especially [as there is] nobody I can report her to because she is the manager."
A Starbucks spokesman responding via the page quickly said that the video "is not reflective of the service our partners provide to our customers every day".
Another post the following day made clear that the company has fired Melissa for her indiscretion.
The spokesman said: "We take this issue seriously; this experience does not represent the high service standards we set for ourselves. This partner no longer works for Starbucks."
Chen added that she had been offered a $100 Starbucks gift card as an apology.
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- Daily Mail