Under usual circumstances, without a global pandemic, numerous parents might encounter stress associated with their roles as caregivers. However, with the added impact of the health crisis and the widespread adoption of lockdown measures, family routines were disrupted as many parents found themselves spending more time at home. Most caregivers had to juggle remote work while simultaneously providing care for their children. This situation has raised concerns about the potential for parental burnout. The objective of this study was to describe parental burnout in mothers and fathers during the COVID-19 lockdowns in Chile and analyze its relationship with possible risk factors such as days in quarantine, perceived impact of COVID-19 on parenting, hours dedicated to weekly paid work, and caregivers’ perception of the need for care of their children. Furthermore, we sought to describe the relationship between parental burnout and coparental cooperation, evaluating the latter as a possible protective factor. An online cross-sectional survey design was used. The sample consisted of 599 people (78.5% mothers) over 18 years old who live in Chile with at least one child. Through a quantitative methodology and using R, multiple regression models were performed with predictive modeling to contrast the hypotheses. The results indicate that the variables related to lockdown, such as days in quarantine and level of involvement of fathers and mothers in parenting due to the pandemic, predict parental burnout. Caregivers’ perception of the need for care of their children also has a significant impact on this phenomenon. In addition, mothers have higher levels of exhaustion than fathers. The number of hours of paid work does not predict parental burnout. Coparenting cooperation in this context can represent a protective factor against chronic stress.