Stability of α-chlorocarbocations
As Oscar Lanzi suggested, both $+M$ and $-I$ applies here, but $\ce{Cl}$ stabilizes carbocation, meaning $+M$ is more effective than $-I$. This fact was confirmed by this peer-reviewed paper (Ref.1):


  The lowering of $\ce{C_\beta–H}$ stretching frequencies in carbocations 1a–d and 2a–c induced by hyperconjugation was tested as a possible probe for estimating the electron donating ability of $\alpha$-substituents. Conclusions are based on the results of high level quantum chemical calculations confirmed with experimental FT-IR spectra. Because the decrease in the $\ce{C_\beta–H}$ stretching frequency is comparable in 1b and in 1c, and in 2b and 2c respectively, it follows that $\alpha$-substitution $\color{red}{\text{by a methyl group}}$ or $\color{red}{\text{by chlorine}}$ stabilizes a carbocation with $\color{red}{\text{almost the same effectiveness}}$.


The effect of the chlorine $n$-electron back donation is evident by a partially double bond character of the $\ce{C+–Cl}$ bond in $\alpha$-chlorocarbocations observed experimentally in IR spectra (Ref.2). In this experiment, FT-IR spectrum of $\ce{Cl3C+}$ cation has displayed the $\ce{C–Cl}$ stretching frequency at $\pu{1040 cm–1}$, which is $\pu{250 cm–1}$ higher than in neutral alkyl chlorides (e.g., characteristic $\ce{C–Cl}$ stretching frequency of $\ce{CCl4}$ is $\pu{785 cm-1}$). This is indicative of partial double bond character of $\ce{C+–Cl}$ bond suggested by the resonance structures: 

$$\ce{Cl2C+-Cl &lt;-&gt; CH2C=Cl+}$$

The pioneering work of Olah and coworkers has also predicted this phenomena by $\ce{^{13}C}$-NMR studies of trihalocarbocations (Ref.3):

$$
\begin{array}{c|c|c|c}
\ce{HCX3} &amp; \delta\ce{^{13}C}\text{ of }\ce{CHX3}  &amp; \ce{^+CX3}  &amp; \delta\ce{^{13}C}\text{ of }\ce{^+CX3} &amp; \Delta \delta\ce{^{13}C} \\
\hline
\ce{HCCl3} &amp; 77.7 &amp; \ce{^+CCl3} &amp; 236.3 &amp; 158.6 \\
\ce{HCBr3} &amp; 12.3 &amp; \ce{^+CBr3} &amp; 207 &amp; 194.7 \\
\ce{HCI3} &amp; -139.7 &amp; \ce{^+CI3} &amp; 95 &amp; 234.7\\
\hline
\end{array}
$$

Olah has suggested that the decreasing trend of $\Delta \delta\ce{^{13}C}$ by going $\ce{I}$ to $\ce{Br}$ to $\ce{Cl}$ is in agreement with the positive charge stabilization by back-bonding in order of $\ce{Cl &gt; Br &gt; I}$.

References:


Milan Mesić, Igor Novak, Dionis E. Sunko, Hrvoj Vančik, "$\ce{C–H}$ Hyperconjugation in $\alpha$-chlorocarbocations," J. Chem. Soc., Perkin Trans. 2 1998, (11), 2371-2374 (https://doi.org/10.1039/A805772I).
Hrvoj Vančik, Ksenija Percač, Dionis E. Sunko, "Chloromethyl cations in cryogenic antimony pentafluoride matrixes and the generation of carbocations from hydrocarbons," J. Am. Chem. Soc. 1990, 112(20), 7418–7419 (https://doi.org/10.1021/ja00176a065).
George A. Olah, Ludger Heiliger, G. K. Surya Prakash, "Stable carbocations. Part 276. Trihalomethyl cations," J. Am. Chem. Soc. 1989, 111(20), 8020–8021 (https://doi.org/10.1021/ja00202a056).