A total of 104 samples of chicken meat acquired on the day of slaughter from two slaughterhouses in northwestern Spain were analyzed. These comprised 26 carcasses and 26 cuts from each of the two establishments. An average load of 5.39 ± 0.61 log10 cfu/g (total aerobic counts) and 4.90 ± 0.40 log10 cfu/g (psychrotrophic microorganisms) were obtained, with differences (p < 0.05) between types of samples and between slaughterhouses. Culturing methods involving isolation based on the UNE-EN-ISO 11290-1:2018 norm and identification of isolates by polymerase chain reaction (PCR) to detect the lmo1030 gene allowed the detection of Listeria monocytogenes in 75 samples (72.1% of the total; 50.0% of the carcasses and 94.2% of the cuts). The 75 isolates, one for each positive sample, were tested for resistance against a panel of 15 antibiotics of clinical interest by the disc diffusion method. All isolates belonged to the serogroup IIa (multiplex PCR assay) and showed resistance to between four and ten antibiotics, with an average value of 5.7 ± 2.0 resistances per isolate, this rising to 7.0 ± 2.1 when strains with resistance and reduced susceptibility were taken together. A high prevalence of resistance was observed for antibiotics belonging to the cephalosporin and quinolone families. However, the level of resistance was low for antibiotics commonly used to treat listeriosis (e.g., ampicillin or gentamicin). Nine different resistance patterns were noted. One isolate with each resistance pattern was tested for its ability to form biofilms on polystyrene during 72 h at 12 °C. The total biovolume of the biofilms registered through confocal laser scanning microscopy (CLSM) in the observation field of 16,078.24 μm2 ranged between 13,967.7 ± 9065.0 μm3 and 33,478.0 ± 23,874.1 μm3, and the biovolume of inactivated bacteria between 0.5 ± 0.4 μm3 and 179.1 ± 327.6 μm3. A direct relationship between the level of resistance to antibiotics and the ability of L. monocytogenes strains to form biofilms is suggested.