We present a close companion search around 16 known early L dwarfs using aperture masking interferometry with Palomar laser guide star adaptive optics (LGS AO). The use of aperture masking allows the detection of close binaries, corresponding to projected physical separations of 0.6-10.0AU for the targets of our survey. This survey achieved median contrast limits of ΔK ∼ 2.3 for separations between 1.2λ/D-4λ/D and ΔK ∼ 1.4 at λ/D. We present four candidate binaries detected with moderate-to-high confidence (90%-98%). Two have projected physical separations less than 1.5AU. This may indicate that tight-separation binaries contribute more significantly to the binary fraction than currently assumed, consistent with spectroscopic and photometric overluminosity studies. Ten targets of this survey have previously been observed with the Hubble Space Telescope as part of companion searches. We use the increased resolution of aperture masking to search for close or dim companions that would be obscured by full aperture imaging, finding two candidate binaries. This survey is the first application of aperture masking with LGS AO at Palomar. Several new techniques for the analysis of aperture masking data in the low signal-to-noise regime are explored.