How to make this script allow the player to move right?

The problem in your code was you were only checking one direction not both.

local cameraHeight = 12
local cameraZOffset = 20
local cameraXChase = 10
local cameraSpeed = .25

local camera = game.Workspace.CurrentCamera
local player = game.Players.LocalPlayer
local RunService = game:GetService('RunService')

local function setupCamera()
    camera.CoordinateFrame = 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

        if cameraX - cameraXChase < playerX then
            camera.CoordinateFrame = camera.CoordinateFrame + Vector3.new(cameraSpeed, 0, 0)
		elseif cameraX - cameraXChase > playerX then -- Adding this here allows for it to check the other direction. All I did was reverse what the if did.
            camera.CoordinateFrame = camera.CoordinateFrame - Vector3.new(cameraSpeed, 0, 0)
        end
    end
end

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

Hope it helps! If this helped please accept this answer so other people can see the solution.