Choosing Random Player Isn't Working. How to Fix?

You should use the method GetPlayers() rather than GetChildren() incase there is a child of game.Players that is not a player:

local players = game.Players:GetPlayers()
if #players > 0 then
    local randomPlayer = players[math.random(1, #players)]
    -- Do Stuff
end

All this error means is that #players equals zero. No players are in the game.

I don't know the context of these lines, but it might be that they're running as soon as the game starts. This would mean that no players are loaded yet, making the table empty. You can fix this with either a loop or an event depending on the situation.

repeat wait(1) until #game.Players:GetPlayers() > 0

Or,

game.Players.PlayerAdded:connect(function(plr)
     --do stuff
end)

And as other people have pointed out, definitely use GetPlayers.

Here's one that I'm using For my game and it works.

local randomplayer = {}
local x
local T = game.Workspace.WaitTime.Value
game.Players.PlayerAdded:connect(function()
    -- What you're doing wrong is that you're making a table with no players even loaded. Doing it this way it will Update the table everytime a player joins.
    local players = game.Players:GetPlayers()
    -------------------------------------------------------



    -- Ignore This VV. But you can use it if you want.
    for _, v in pairs (players) do
        table.insert(randomplayer, v.Name)
    end

    while wait(5) do
        local randomnum = math.random(#randomplayer)
        local randomname = randomplayer[randomnum]
        local randomplayer = game.Players:FindFirstChild(randomname)
        if randomplayer then
            print(randomplayer)
            game.Workspace.TheChosenOne.Value = randomplayer
        end
    end
end)

The problem with your script is that the table is empty and scripts always run before the character is even loaded so you make the script wait with the:

game.Players.PlayerAdded:connect(function()
    local players = game.Players:GetPlayers()
end)