To get the Unbroken Chain trophy you need to match only one type of chips 5 times in a row (then 8, 10, 11, and finally 12 times). It means you can't match other types of chips in-between or the chain will be broken. That's why it's called Unbroken Chain.
The counter on the trophy records every move you make on the match-3 level board. When you break the chain of matches made with identical chips by a match with another type of chips, the counter is reset to 1 and starts counting a new chain with a new type of chips. For example if you make several matches with red chips and then match blue chips, the counter will be reset.
So if you do not make an intentional attempt to get this achievement you will commonly see in this trophy for example 1/8(or 2/8 or 3/8, etc) because it resets the counter each time you make a move using another type of chips.
You can check an example of an Unbroken Chain here.
Please also watch this video, it shows how to make an Unbroken Chain: