To reach nominal bunch compression and FEL performance of SwissFEL with stable beam conditions for the users, less than 40fs relative rms jitter is required from the injector. Phase noise measurement of the gun laser oscillator shows an exceptional 30 fs integrated rms jitter. We present these measurements and analyze the contribution to the timing jitter and drift from the rest of the laser chain. These studies were performed at the SwissFEL Injector Test Facility, using the rising edge of the Schottky-scan curve and on the laser system using fast digital signal analyzer and photodiode, revealing a residual jitter of 150 fs at the cathode from the pulsed laser amplifier and beam transport, measured at 10Hz. Spectrally resolved cross-correlation technique will also be reviewed here as a future solution of measuring timing jitter at 100 Hz directly against the pulsed optical timing link with an expected resolution in the order of 50 fs. This device will provide the signal for feedback systems compensating for long term timing drift of the laser for the gun as well as for the pulsed lasers at the experimental stations.