Didn't Chelsea get rid of him when they should have kept him?

No his Father/Agent wanted him to leave and go to Real Madrid, Chelsea only agreed to sell him at their price, which was 35 million Euros. Robben was loved by the fans but is only fit for about 50% of games, he said this on leaving Chelsea;

Robben: “I knew on the first day of the pre-season that Chelsea agreed to sell me to Real Madrid. And I really wanted to go. Chelsea made the negotiations very hard, though. It took 7 weeks, all in all. Some people at Chelsea didn’t want to see me go. But two people were ok for me to leave, so I left. But yes, I did leave Chelsea under weird conditions and similar with Real Madrid. I never had the chance to thank the fans.”

We'd still welcome him back with open arms and he is an extraordinarily talented player,

He's a great player, but spends more time on the bench than on the field through injury. He's got glass ankles.