How much thrust do you lose by putting chevrons on a engine?
The main purpose of the Chevrons is the reduction of engine noise. During research into this, NASA tested a number of configurations under simulated flying conditions and measured the nozzle thrust coefficient given by,

$C_{T_{r}} = \frac{F^{d}_{g}}{F^{i}_{g}}$

where,

$F^{d}_{g}$ is the measure gross thrust and 

$F^{i}_{g}$ is the ideal gross thrust

We have,

$F^{i}_{g}$ = .{m}$_{c} v_{i,c}$ + .{m}$_{f} v_{i,f}$

where .{m}$_{c}$ is mass flow rate of core, .{m}$_{f}$ is mass flow rate of fan and $v_{i,c}$ and $v_{i,f}$ are core and fan ideally expanded jet velocities respectively.

The reduction in nozzle thrust coefficient was compared with baseline (no modifications) configuration.


Source: NASA/TM—2000-209948

The configuration used in engine (Chevrons in the fan and nothing in the nozzle produced the lowest loss of thrust coefficient, 0.18.

However, the noise reduction was lesser in this configuration compared to the others. Further modifications have been carried out in the chevrons used in production engines (they are rounded, for one). So, the noise reduction has been obviously improved, though the minimal loss of thrust would've been maintained. 

Note: All data from Acoustics and Thrust of Separate-Flow Exhaust Nozzles With Mixing Devices for High-Bypass-Ratio Engines, Naseem H. Saiyed, Kevin L. Mikkelsen and James E. Bridges, Prepared for Prepared for the
Sixth Aeroacoustics Conference and Exhibit, Lahaina, Hawaii, June 12–14, 2000