Mr Pichai, who rose from humble beginnings in India, was appointed Google's CEO in 2015.
The inspiration for Chloe's letter had been internet research showing Google's offices including bean bags, go karts and slides but she also highlighted a keen interest in computers in her application.
Chloe also admitted to an interest in a job in a chocolate factory or as a swimmer at the Olympics in the letter, and Mr Pichai's reply said "if she kept working hard and following her dreams, she could accomplish everything she set her mind to."
Mr Bridgewater said he and his wife Julie, a HR advisor, had seen Chloe's business acumen in action already.
Besides her love of swimming - 20 lengths on Tuesdays with her mum - Chloe has also volunteered to clean the kitchen for 20p, he said.
"She is only young so she needs to play with her friends, jump on a trampoline but whenever she shows an interest in something else - like this letter - we want to encourage her," Andy said.