Initiate chin-up by learning to pull first with the shoulder blades (scapulae) first. A basic principle in biomechanics is that force production is a product of joint summation.
Using the scapulae retractors to initiate the movement produces more force. Concentrate on moving the elbows back and down. Most trainees overemphasise pulling with the elbow flexors to initiate the chin-up.
Once you have retracted the scapulae, concentrate on elbowing the gut of someone who is standing behind you. That action will activate the latissimus dorsi and the teres major, which are powerful shoulder extensors.