Second hand bike. GTZR3000

Shimano 105 9 speedshifter  

9 speed rear group shimano  

9 speed tiagra rear derailleur 

The bike runs fine on large front ring, shifting is perfect.

When I change for an incline to the smaller front ring and apply pedal presure the chain comes straignt off. On a stand without pressure resistance on the drive train, everything moves perfectly. Back on the road and again and pedal pressure sends the chain off.

Can anyone advise if they are aware of potential reason why?