Context : The bright low-mass X-ray binary ( LMXB ) GX 13+1 is one of the most peculiar Galactic binary systems .
A periodicity of 24.27 d with a formal statistical error of 0.03 d was observed in its power spectrum density obtained with RXTE All Sky Monitor ( ASM ) data spanning 14 years .

Aims : Starting from a recent study , indicating GX 13+1 as a possible dipping source candidate , we systematically searched for periodic dips in the X-ray light curves of GX 13+1 from 1996 up to 2013 using RXTE/ASM , and MAXI data to determine for the first time the X-ray orbital ephemeris of GX 13+1 .

Methods : We searched for a periodic signal in the ASM and MAXI light curves , finding a common periodicity of 24.53 d. We folded the 1.3-5 keV and 5-12.1 keV ASM light curves and the 2-4 and 4-10 keV MAXI light curves at the period of 24.53 d finding a periodic dip .
To refine the value of the period we used the timing technique dividing the ASM light curve in eight intervals and the MAXI light curve in two intervals , obtaining four and two dip arrival times from the ASM and MAXI light curves , respectively .

Results : We improved the X-ray position of GX 13+1 using a recent Chandra observation .
The new X-ray position is discrepant by \sim 7 \arcsec from the previous one , while it is compatible with the infrared and radio counterpart positions .
We detected an X-ray dip , that is totally covered by the Chandra observation , in the light curve of GX 13+1 and showed , a-posteriori , that it is a periodic dip .
We obtained seven dip arrival times from ASM , MAXI , and Chandra light curves .
We calculated the delays of the detected dip arrival times with respect to the expected times for a 24.52 d periodicity .
Fitting the delays with a linear function we find that the orbital period and the epoch of reference of GX 13+1 are 24.5274 ( 2 ) days and 50,086.79 ( 3 ) MJD , respectively .
Adopting a quadratic ephemeris we do not improve the fit .
The inferred orbital period derivative of 8 ( 37 ) \times 10 ^ { -8 } s/s , with the error at 68 % confidence level , does not allow us to constrain the orbital evolution of the binary system .

Conclusions : We demonstrated the existence of periodic dips in the ASM and MAXI light curves estimating that the orbital period of GX 13+1 is 24.5274 ( 2 ) d. GX 13+1 has the longest known orbital period for a Galactic neutron star LMXB powered by Roche lobe overflow .