In this work, we propose and demonstrate a module to linearly add an arbitrary amount of continuous (reset-free) phase delay to an optical signal. The proposed endless optical phase delay (EOPD) uses an optical IQ modulator and control electronics (CE) to add the desired amount of phase delay that can continuously increase with time. In order to adjust for the bias voltages and control voltage amplitudes in the EOPD, some of which may be time varying, a multivariate gradient descent algorithm is used. The EOPD has been demonstrated experimentally, and its use in a high-capacity data center interconnect (DCI) application has been outlined in this letter. The EOPD may find its use in many other applications that require precise phase/frequency adjustments in real-time.