An independent run by Linc Chafee would have real traction in RI, but only if he promised to caucus with the Dems. He could potentially beat Whitehouse under those circumstances. If Reed were tapped for a cabinet post in a Democratic administration, he could also take that seat.
This scenario has a lot of ifs though - if Reed leaves or Whitehouse can't win re-election, if Chafee decides to run for Senate again, if he runs as an independent and if he promises to caucus with the Dems. Nevertheless, it could happen.
I think Whitehouse would have to screw up for that to happen. Chafee is loved, but not so loved that Rhode Island would boot out a relatively popular, if one-term, incumbent to get him back in the Senate. If Reed vacates his seat, though, Chafee would be easily favored as an independent over any Democrat and would also be easily favored in the Democratic primary should he choose to run as one. I don't think he'd even have to pledge to caucus with the Democrats, just pledge not to caucus with the Republicans.