The excellent compliance and large range of motion of soft actuators controlled by fluid pressure has lead to strong interest in applying devices of this type for biomimetic and human-robot interaction applications. However, in contrast to soft actuators fabricated from stretchable silicone materials, conventional technologies for position sensing are typically rigid or bulky and are not ideal for integration into soft robotic devices. Therefore, in order to facilitate the use of soft pneumatic actuators in applications where position sensing or closed loop control is required, a soft pneumatic bending actuator with an integrated carbon nanotube position sensor has been developed. The integrated carbon nanotube position sensor presented in this work is flexible and well suited to measuring the large displacements frequently encountered in soft robotics. The sensor is produced by a simple soft lithography process during the fabrication of the soft pneumatic actuator, with a greater than 30% resistance change between the relaxed state and the maximum displacement position. It is anticipated that integrated resistive position sensors using a similar design will be useful in a wide range of soft robotic systems.