attempt to index nil with 'Clone' ?

local petModel = pets:FindFirstChild(chosenPet.petName):Clone()
petModel:PivotTo(CFrame.new(0, 0, 0))
petModel.Parent = eggViewport
local cameraPet = Instance.new("Camera")
cameraPet.Parent = eggViewport
cameraPet.CFrame = CFrame.new(0,0, -3.3) * CFrame.Angles(0, math.rad(180), 0)
eggViewport.CurrentCamera = cameraPet
tweenService:Create(eggViewport, TweenInfo.new(0.7), {Size = UDim2.new(0.236, 0,0.494, 0)}):Play()	
eggViewport.NameLabel.Text = chosenPet.petName
eggViewport.NameLabel.Visible = true
eggViewport.RarityLabel.Text = chosenPet.Rarity
eggViewport.RarityLabel.Visible = true
task.wait(1.5)
tweenService:Create(eggViewport, TweenInfo.new(0.3), {Size = UDim2.fromScale(0, 0)}):Play()
task.wait(0.3)
eggViewport.NameLabel.Visible = false
eggViewport.RarityLabel.Visible = false		
for _, v in pairs(player:GetChildren()) do
	if v:IsA("ScreenGui") or v ~= eggSystemSS then
		v.Enabled = true
	end
end

end

Without having more context to your code, it's hard to judge what exactly is going on. From the error stated in your title, it appears that local petModel = pets:FindFirstChild(chosenPet.petName):Clone() is causing your error. To narrow it down, the children of pets does not contain the pet chosenPet.petName, causing it to be nil, which then causes your error.

To try and fix this, I suggest printing chosenPet.petName and see what you get from that, then if that seems correct, (make sure you are in studio) print pets:GetChildren() which will return of all the child objects under pets.

Just to confirm, pets is an object in your explorer/game, correct? If pets is a table, the fix above is wrong, and you will need to supply some context code as to what exactly pets is.