Major spoilers for the whole game (duh)
In TJ's route we are given a treasure hunt, where the final reward is a drawing of Chase drowning Sydney while TJ watches. This is further confirmed by Micha telling us that he had a dream where he was being drowned by Chase and also TJ telling us in Flynn's route that he saw 2 brown-furred bodies in the water that day.
Even though Chase thought Sydney was being very "weird" the last 6 months (possibly because Samuel was possesing Sydney at the time) and also said that he was glad that he died (because of the "weirdness"), it's still quite uncharacteristic of him to just go ahead and murder him. (he is very indecisive, so he would never be able to make such a drastic choice)
I assume the murder was done by the same voice that killed Flynn in TJ's route, as they both appear to share the unreasonableness of it all. Chase did technically kill Sydney, but he really didn't want to. It was all because of that new voice. We know that the spirits possesing Chase can take control (Like when Chase is about to be killed by Brian), and since the new voice is much stronger than Sam, i'm certain it could force Chase to do something like murder.
And to put the final nail in the coffin: how would Chase end up with Sam's ghost if he didn't kill Syd? We know Sam changes hosts to the person that kills the current host (Sam->Syd's dad->Syd), so how would Chase end up with him if the person in the lake was someone else?