I really liked Chase, and I think he is by far the dropped thread that feels like the largest loss.
He was sort of fucked by the end of Season 3, though, in multiple ways. He was snookered. If he broke up with Kim, Jack would've hated him for letting Kim down, and that relationship would've been shattered and reset to zero, basically. If he stayed with Kim and then appeared in Season 4, there would've been the "where's Kim?" question, and after two seasons of desperately trying to make a post-kidnapping Kim work, they were finally ready to be rid of her in Season 4. So Chase had to go as well if Kim was going. Then they cut off his hand, which basically removed him from field work, though obviously that decision was taken after they'd decided to do away with him..
Still. In many ways I would've very much liked, come Season 4, Chase to be in what became the Curtis role. Head of Field Ops, under that lady whose name I forget. Jack fired, Chase took his job, Chase dumped Kim, that relationship shattered. Jack comes back as part of DOD, fireworks ensue.