We present what is believed to be the first direct measurement of the relative timing jitter between the two parallel pulse trains of a two-branch femtosecond erbium-doped fiber laser, operated without active stabilization. The system provides independently tunable pulses in the near infrared with durations down to 13 fs. Using an interferometric optical cross-correlator, the phase-noise spectral density is measured with high sensitivity in a range from 1 Hz up to the Nyquist frequency of 24.5 MHz. We find an integrated jitter of 11 attoseconds directly after the amplifier stages and 43 as after propagation through free-space optics and nonlinear fibers for frequency conversion.