Aphetto Alchemist does not have summoning sickness.
Steps
Activate Chandra's second loyalty ability by putting zero loyalty counters on it, creating two 1/1 Elemental creature tokens with haste.
When the Elementals enter the battlefield, Intruder Alarm triggers twice.
Resolve the first trigger, untapping all creatures.
Activate Aphetto Alchemist by tapping it, untapping The Chain Veil.
Resolve the second Intruder Alarm trigger, untapping all creatures.
Activate Aphetto Alchemist by tapping it, untapping target artifact or creature.
Activate Ashnod's Altar twice by sacrificing the two Elemental tokens, adding ({C} magic symbol) ({C} magic symbol) ({C} magic symbol) ({C} magic symbol) .
Activate The Chain Veil by paying ({4} magic symbol) and tapping it, allowing you an additional activation of your planeswalkers' loyalty abilities this turn.
Repeat.
Results
Infinite activations of loyalty abilities of all other Planeswalkers you control.