Chain levels go from 0-3, so yeah once you level up 3 times you're at max.
Consulting my Ultimania guide the chances of level up are calculated on chance:
Code:
Chain level 0
6 kills 40%
7 kills 60%
8 kills 80%
9 kills 90%
10 kills 100%
Chain level 1
6 kills since level up 20%
7 kills since level up 30%
8 kills since level up 50%
9 kills since level up 60%
10 kills since level up 100%
Chain level 2
6 kills since level up 10%
7 kills since level up 20%
8 kills since level up 30%
9 kills since level up 40%
10 kills since level up 100%
Where the % represents the chances that your chain level will increase. Once you're at Chain level 3 (max) you won't advance again.