Background/Objectives: Lacticaseibacillus rhamnosus HN001 (HN001) is a probiotic strain widely studied for its potential to improve human health. Previous studies have demonstrated promising results for HN001 in the improvement of mental well-being, particularly in terms of increased happiness and support for stress management in healthy adults. Methods: To further explore these findings, a double-blind, placebo-controlled trial was conducted with 120 participants aged ≥ 18 years with mild to high stress measured by the Perceived Stress Scale (PSS). The participants were randomly assigned to receive either HN001 or placebo for 28 days. Psychological assessments, including the Oxford Happiness Questionnaire (OHQ), were completed at baseline, day 14, and day 28. Secondary outcomes included changes in PSS scores, as well as depression, anxiety, stress, and total score levels measured by the DASS-21 questionnaire. Results: While not statistically significant, participants who received HN001 showed an improvement in OHQ (mean change, 13.3) and PSS total scores (mean change, −8.1) over time compared with the placebo group (mean change, 10.2 and −6.6, respectively). Furthermore, 39% of the participants moved from not happy to happy, compared with only 29% in the placebo group. Post-hoc analysis showed a statistically significant interaction between intervention and study day for OHQ and PSS total scores, with p-values of 0.014 and 0.043, respectively. No adverse effects were observed. Conclusions: HN001 showed improvements in both happiness and PSS scores. Furthermore, sex subgroup analysis revealed statistically significant differences in both outcomes, emphasizing the need for larger and longer intervention studies.