We present a 324.5MHz image of the NOAO Bo\"otes field that was made using Very Large Array (VLA) P-band observations. The image has a resolution of 5.6x5.1arcsec, a radius of $2.05^\circ$ and a central noise of ~0.2mJy\beam. Both the resolution and noise of the image are an order of magnitude better than what was previously available at this frequency and will serve as a valuable addition to the already extensive multiwavelength data that are available for this field. The final source catalogue contains 1370 sources and has a median 325 to 1400MHz spectral index of -0.72. Using a radio colour-colour diagram of the unresolved sources in our catalogue, we identify 33 megahertz peaked-spectrum (MPS) sources. Based on the turnover frequency linear size relation for the gigahertz peaked-spectrum (GPS) and compact steep-spectrum (CSS) sources, we expect that the MPS sources that are compact on scales of tens of milliarcseconds should be young radio loud active galactic nuclei at high (z>2) redshifts. Of the 33 MPS sources, we were able to determine redshifts for 24, with an average redshift of 1.3. Given that five of the sources are at z>2, that the four faint sources for which we could not find redshifts are likely at even higher redshifts and that we could only select sources that are compact on a scale of ~5arcsec, there is encouraging evidence that the MPS method can be used to search for high-redshift sources.