which chamber of the U. S. Congress does the balance of power depend on the outcome of one state's runoff election?

The Senate

Explanation:

There will be a runoff election in the State of Georgia on the 5th of January 2021 to decide who will sit on both the senate seats of Georgia. These seats will decide the party that has the majority in the Senate.

As a result it is a very important election as it will impact how effective the incoming President Joe Biden will be in passing laws. If the Democrats win, Joe Biden will be in a better position and if not, he could have a much tougher presidency with the Republicans blocking some of his bills.

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