We present an overview of the initial results from the Chandra Planetary Nebula Survey (CHANPLANS), the first systematic (volume-limited) Chandra X-Ray Observatory survey of planetary nebulae (PNe) in the solar neighborhood. The first phase of CHANPLANS targeted 21 mostly high-excitation PNe within 1.5kpc of Earth, yielding four detections of diffuse X-ray emission and nine detections of X-ray-luminous point sources at the central stars (CSPNe) of these objects. Combining these results with those obtained from Chandra archival data for all (14) other PNe within 1.5kpc that have been observed to date, we find an overall X-ray detection rate of 70% for the 35 sample objects. Roughly 50% of the PNe observed by Chandra harbor X-ray-luminous CSPNe, while soft, diffuse X-ray emission tracing shocks - in most cases, "hot bubbles" - formed by energetic wind collisions is detected in 30%; five objects display both diffuse and point-like emission components. The presence (or absence) of X-ray sources appears correlated with PN density structure, in that molecule-poor, elliptical nebulae are more likely to display X-ray emission (either point-like or diffuse) than molecule-rich, bipolar, or Ring-like nebulae. All but one of the point-like CSPNe X-ray sources display X-ray spectra that are harder than expected from hot (100kK) central stars emitting as simple blackbodies; the lone apparent exception is the central star of the Dumbbell nebula, NGC6853. These hard X-ray excesses may suggest a high frequency of binary companions to CSPNe. Other potential explanations include self-shocking winds or PN mass fallback. Most PNe detected as diffuse X-ray sources are elliptical nebulae that display a nested shell/halo structure and bright ansae; the diffuse X-ray emission regions are confined within inner, sharp-rimmed shells. All sample PNe that display diffuse X-ray emission have inner shell dynamical ages ≲ 5 × 10³yr, placing firm constraints on the timescale for strong shocks due to wind interactions in PNe. The high-energy emission arising in such wind shocks may contribute to the high excitation states of certain archetypical "hot bubble" nebulae (e.g., NGC2392, 3242, 6826, and 7009).