There is a (now) fairly standard interaction with lists on both iOS and Android where the user can slide an item to one side to reveal contextual actions for that item.
Some interfaces even have different selections depending on which direction the menu item is moved.
Unless you are expecting your user to be deleting more than around 10 chats at once, this method should be easy enough for them to manage.
If you are expecting your user to be managing more than around 10 deletes at once, then it's probably best that you allow them to enter some sort of management mode where they have access to new controls allowing them so select multiple chats and perform a single action on all chats selected - This could be in the form of an "Edit" mode as Mr.Swaggalicious has suggested in the comments.
It is important to note that each of these methods will suit different management styles - the swipe is perfect for small numbers of deletions while, for large numbers of deletions the management mode is more suitable. If you think your users may be requiring both ends of the spectrum then it's not unreasonable to include both methods.