The most important issue is how to give customer confidence that the payment information they provide is protected. From this perspective, chat window is the worst possible option. A person will never feel secure giving out their private data over a chat channel. Event you say it's absolutely secure.

You may add Checkout button to chat window. This button should open a separate screen where user can to provide their payment information. There you may emphasize how the data are protected, e.g. SSL seal, pen-test certification etc. You may keep the chat window on that screen, but it must be visually separated from the payment information delivering a message that payment does not go through the chat.

The most important issue is how to give customer confidence that the payment information they provide is protected. From this perspective, chat window is the worst possible option. A person will never feel secure giving out their private data over a chat channel. Even if you say it's absolutely secure.

You may add Checkout button to chat window. This button should open a separate screen where user can to provide their payment information. There you may emphasize how the data are protected, e.g. SSL seal, pen-test certification etc. You may keep the chat window on that screen, but it must be visually separated from the payment information delivering a message that payment does not go through the chat.