Searches for supersymmetric electroweakinos have entered a crucial phase, as the integrated luminosity of the Large Hadron Collider is now high enough to compensate for their weak production cross-sections. Working in a framework where the neutralinos and charginos are the only light sparticles in the Minimal Supersymmetric Standard Model, we use GAMBIT to perform a detailed likelihood analysis of the electroweakino sector. We focus on the impacts of recent ATLAS and CMS searches with 36 fb$^{-1}$ of 13 TeV proton-proton collision data. We also include constraints from LEP and invisible decays of the $Z$ and Higgs bosons. Under the background-only hypothesis, we show that current LHC searches do not robustly exclude any range of neutralino or chargino masses. However, a pattern of excesses in several LHC analyses points towards a possible signal, with neutralino masses of $(m_{\tilde{\chi}_1^0}, m_{\tilde{\chi}_2^0}, m_{\tilde{\chi}_3^0}, m_{\tilde{\chi}_4^0})$ = (8-155, 103-260, 130-473, 219-502) GeV and chargino masses of $(m_{\tilde{\chi}_1^{\pm}}, m_{\tilde{\chi}_2^{\pm}})$ = (104-259, 224-507) GeV at the 95% confidence level. The lightest neutralino is mostly bino, with a possible modest Higgsino or wino component. We find that this excess has a combined local significance of $3.5\sigma$, subject to a number of cautions. We briefly consider the implications for dark matter, finding that the correct relic density can be obtained through the Higgs-funnel and $Z$-funnel mechanisms, even assuming that all other sparticles are decoupled. All samples, GAMBIT input files and best-fit models from this study are available on Zenodo.