Events with no charged particles produced between the two leading jets are studied in proton-proton collisions at $\sqrt{s}$ = 7 TeV. The jets were required to have transverse momentum $p_\mathrm{T}^{\text{jet}}$ > 40 GeV and pseudorapidity 1.5 $<|\eta^{\text{jet}}| <$ 4.7, and to have values of $\eta^{\text{jet}}$ with opposite signs. The data used for this study were collected with the CMS detector during low-luminosity running at the LHC, and correspond to an integrated luminosity of 8 pb$^{-1}$. Events with no charged particles with $p_\mathrm{T}$ > 0.2 GeV in the interval -1 < $\eta$ < 1 between the jets are observed in excess of calculations that assume no color-singlet exchange. The fraction of events with such a rapidity gap, amounting to 0.5-1% of the selected dijet sample, is measured as a function of the $p_\mathrm{T}$ of the second-leading jet and of the rapidity separation between the jets. The data are compared to previous measurements at the Tevatron, and to perturbative quantum chromodynamics calculations based on the Balitsky-Fadin-Kuraev-Lipatov evolution equations, including different modelings of the non-perturbative gap survival probability.