Instead of the commonly used approach of conducting controlled experiments to estimate chilling and heat requirements (CR and HR) of fruit trees, the statistical method of Partial Least Squares (PLS) regression was applied to identify the CR and HR of apricot (Prunus armeniaca L.) in Beijing, China by correlating first flowering dates of apricot with daily chilling and heat accumulation during 1963–2010. Three common chilling models (the 0–7.2 ◦C, Utah and Dynamic Models) and one forcing model (the Growing Degree Hour Model) were used to convert daily temperature data into daily chill and heat accumulation rates. The results indicated that PLS regression analysis is a useful approach to estimate the CR and HR of fruit trees wherever phenology and climate observations have been conducted for long periods. Use of all chilling models indicated similar chilling periods for apricot in Beijing (mid-September to early March), while the identified forcing period started in early January and extended to the first flowering date for each year. The Dynamic Model appeared to be the most accurate model with smallest year-to-year variation in chill accumulated during the chilling period (coefficient of variation of only 7.5%). Using the Dynamic Model for chill, and the Growing Degree Hour Model for heat quantification, the CR of apricot in Beijing was determined at 75 ± 6 Chill Portions (CP) and the HR at 3055 ± 938 Growing Degree Hours (GDH).