Weird Camera Shake? [UNANSWERED]

Let me explain what's wrong.

Your problem lies in the following lines:

if cameraX - cameraXChase < playerX then
    camera.CoordinateFrame = camera.CoordinateFrame + Vector3.new(cameraSpeed, 0, 0) -- Moves camera right
elseif cameraX - cameraXChase > playerX then
    camera.CoordinateFrame = camera.CoordinateFrame - Vector3.new(cameraSpeed, 0, 0) -- Moves camera left
end

The first line checks if the camera is left of where you want it, the second line checks if the camera is right of where you want it, one of these will always return true.

When it reaches the closest point the camera will move back and forth as it changes to the left and right of where you want it.

To fix this, you should check the cameras position + the move speed like so:

local cameraX = camera.CoordinateFrame.p.X - cameraXChase -- simplified this variable since you - cameraXChase always

if cameraX + cameraSpeed < playerX then
    camera.CFrame = camera.CFrame + Vector3.new(cameraSpeed, 0, 0) -- Moves camera right
elseif cameraX - cameraSpeed > playerX then
    camera.CFrame = camera.CFrame - Vector3.new(cameraSpeed, 0, 0) -- Moves camera left
else
	-- move to the char
end

This stops the jittering effect.

Lastly we should move the camera to the ideal location like so:

camera.CFrame = camera.CFrame + Vector3.new(playerX - cameraX, 0, 0)
											-- minus cameraX so it's moved to
											-- the ideal position for
											-- the player

The full edited code is listed below:

-- Camera setup

local cameraHeight = 12
local cameraZOffset = 20
local cameraXChase = 10
local cameraSpeed = 0.25

local camera = game.Workspace.CurrentCamera
camera.CameraType = Enum.CameraType.Scriptable -- Is this necessary for you?
local player = game.Players.LocalPlayer
local RunService =game:GetService("RunService")

local function setupCamera()
    camera.CFrame = CFrame.new(Vector3.new(0,cameraHeight,cameraZOffset),Vector3.new(0, cameraHeight, 0))
end

setupCamera()
player.CharacterAdded:connect(setupCamera)

local function onUpdate()
    if player.Character and player.Character:FindFirstChild("Torso") then
        local playerX = player.Character.Torso.Position.X
        local cameraX = camera.CoordinateFrame.p.X - cameraXChase

        if cameraX + cameraSpeed < playerX then
            camera.CFrame = camera.CFrame + Vector3.new(cameraSpeed, 0, 0) -- Moves camera right
        elseif cameraX - cameraSpeed > playerX then
            camera.CFrame = camera.CFrame - Vector3.new(cameraSpeed, 0, 0) -- Moves camera left
		else
			camera.CFrame = camera.CFrame + Vector3.new(playerX - cameraX, 0, 0)
        end
    end
end

RunService:BindToRenderStep("Camera",Enum.RenderPriority.Camera.Value, onUpdate)